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1. Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators Abatangelo, Lauraet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt594",{id:"formSmash:items:resultList:0:j_idt594",widgetVar:"widget_formSmash_items_resultList_0_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Felli, VeronicaHillairet, LucLéna, CorentinStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators2019In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 9, no 2, p. 379-427Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:0:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_0_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov–Bohm operators with two colliding poles moving on an axis of symmetry of the domain.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications Abatangelo, Lauraet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt594",{id:"formSmash:items:resultList:1:j_idt594",widgetVar:"widget_formSmash_items_resultList_1_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Felli, VeronicaLéna, CorentinStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications2020In: ESAIM. COCV, ISSN 1292-8119, E-ISSN 1262-3377Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:1:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_1_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_1_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:1:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_1_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:1:j_idt854:0:fullText"});}); 3. Asymptotic distribution of zeros of a certain class of hypergeometric polynomials Abathun, Addisalem PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt591",{id:"formSmash:items:resultList:2:j_idt591",widgetVar:"widget_formSmash_items_resultList_2_j_idt591",onLabel:"Abathun, Addisalem ",offLabel:"Abathun, Addisalem ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Asymptotic distribution of zeros of a certain class of hypergeometric polynomials2014Licentiate thesis, monograph (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:2:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_2_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The thesis consists of two papers, both treating hypergeometric polynomials, and a short introduction. The main results are as follows.In the first paper,we study the asymptotic zero distribution of a family of hypergeometric polynomials in one complex variable as their degree goes to infinity,using the associated differential equations that hypergeometric polynomials satisfy. We describe in particular the curve complex on which the zeros cluster, as level curves associated to integrals on an algebraic curve derived from the equation. The new result is first of all that we are able to formulate results on the location of zeros of generalized hypergeometric polynomials in greater generality than before (earlier results are mainly concerned with the Gauss hypergeometric case.) Secondly, we are able to formulate a precise conjucture giving the asymptotic behaviour of zeros in the generalized case of our polynomials, which covers previous results.In the second paper we partly prove one of the conjectures in the first paper by using Euler integral representation of the Gauss hypergeometric functions together with the Saddle point method.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 4. Asymptotic Distribution of Zeros of a Certain Class of Hypergeometric Polynomialsd Abathun, Addisalem PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt591",{id:"formSmash:items:resultList:3:j_idt591",widgetVar:"widget_formSmash_items_resultList_3_j_idt591",onLabel:"Abathun, Addisalem ",offLabel:"Abathun, Addisalem ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt594",{id:"formSmash:items:resultList:3:j_idt594",widgetVar:"widget_formSmash_items_resultList_3_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Addis Ababa University, Ethiopia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bøgvad, RikardStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Asymptotic Distribution of Zeros of a Certain Class of Hypergeometric Polynomialsd2016In: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 16, no 2, p. 167-185Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:3:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_3_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the asymptotic behavior of the zeros of a family of a certain class of hypergeometric polynomials [GRAPHICS] , using the associated hypergeometric differential equation, as the parameters go to infinity. The curve configuration on which the zeros cluster is characterized as level curves associated with integrals on an algebraic curve. The algebraic curve is the hypergeometrc differential equation, using a similar approach to the method used in Borcea et al. (Publ Res Inst Math Sci 45(2):525-568, 2009). In a specific degenerate case, we make a conjecture that generalizes work in Boggs and Duren (Comput Methods Funct Theory 1(1):275-287, 2001), Driver and Duren (Algorithms 21(1-4):147-156, 1999), and Duren and Guillou (J Approx Theory 111(2):329-343, 2001), and present experimental evidence to substantiate it.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. ZEROS OF A CERTAIN CLASS OF GAUSS HYPERGEOMETRIC POLYNOMIALS Abathun, Addisalem PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt591",{id:"formSmash:items:resultList:4:j_idt591",widgetVar:"widget_formSmash_items_resultList_4_j_idt591",onLabel:"Abathun, Addisalem ",offLabel:"Abathun, Addisalem ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt594",{id:"formSmash:items:resultList:4:j_idt594",widgetVar:"widget_formSmash_items_resultList_4_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Addis Ababa University, Ethiopia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bøgvad, RikardStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); ZEROS OF A CERTAIN CLASS OF GAUSS HYPERGEOMETRIC POLYNOMIALS2018In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 68, no 4, p. 1021-1031Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:4:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_4_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We prove that as n -> infinity, the zeros of the polynomial F-2(1) 9-n, (an + 2) (an + 1) ; z] cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999-2001) to the case of a complex parameter alpha and partially proves a conjecture made by the authors in an earlier work.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 6. On the decomposition of D-modules over a hyperplane arrangement Abebaw, Tilahun PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt591",{id:"formSmash:items:resultList:5:j_idt591",widgetVar:"widget_formSmash_items_resultList_5_j_idt591",onLabel:"Abebaw, Tilahun ",offLabel:"Abebaw, Tilahun ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the decomposition of D-modules over a hyperplane arrangement2007Licentiate thesis, monograph (Other academic)7. Decomposition of D-modules over a hyperplane arrangement in the plane Abebaw, Tilahun PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt591",{id:"formSmash:items:resultList:6:j_idt591",widgetVar:"widget_formSmash_items_resultList_6_j_idt591",onLabel:"Abebaw, Tilahun ",offLabel:"Abebaw, Tilahun ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt594",{id:"formSmash:items:resultList:6:j_idt594",widgetVar:"widget_formSmash_items_resultList_6_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bogvad, RikardStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Decomposition of D-modules over a hyperplane arrangement in the plane2010In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 48, no 2, p. 211-229Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:6:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_6_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Let alpha(1), alpha(2),..., alpha(m) be linear forms defined on C-n and X = C-n\boolean OR(m)(i=1) V(alpha(i)), where V(alpha(i))={p is an element of C-n : alpha(i)(p)=0}. The coordinate ring O-X of X is a holonomic A(n)-module, where A(n) is the nth Weyl algebra and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a "" twisted"" variant of this An- module which is also holonomic. Define M-alpha(beta) to be the free rank-1 C[x](alpha)-module on the generator alpha(beta) (thought of as a multivalued function), where alpha(beta)=alpha(beta 1)(1),..., alpha(beta m)(m) and the multi-index beta=(beta(1),...,beta(m))is an element of C-m. Our main result is the computation of the number of decomposition factors of M-alpha(beta) and their description when n-2.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:6:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 8. Decomposition factors of D-modules on hyperplane configurations in general position Abebaw, Tilahun PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt591",{id:"formSmash:items:resultList:7:j_idt591",widgetVar:"widget_formSmash_items_resultList_7_j_idt591",onLabel:"Abebaw, Tilahun ",offLabel:"Abebaw, Tilahun ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt594",{id:"formSmash:items:resultList:7:j_idt594",widgetVar:"widget_formSmash_items_resultList_7_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics. Addis Ababa University, Ethiopia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bøgvad, RikardStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Decomposition factors of D-modules on hyperplane configurations in general position2012In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, no 8, p. 2699-2711Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:7:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_7_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Let alpha(1), ... , alpha(m) be linear functions on C-n and X = C-n \ V(alpha), where alpha = Pi(m)(i=1) alpha(i) and V(alpha) = {p is an element of C-n : alpha(p) = 0}. The coordinate ring O-X = C[x](alpha) of X is a holonomic A(n)-module, where A(n) is the n-th Weyl algebra, and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a twisted variant of this A(n)-module which is also holonomic. Define M-alpha(beta) to be the free rank 1 C[x](alpha)-module on the generator alpha(beta) (thought of as a multivalued function), where alpha(beta) = alpha(beta 1)(1) ... alpha(beta m)(m) and the multi-index beta = (beta(1), ... , beta(m)) is an element of C-m. It is straightforward to describe the decomposition factors of M-alpha(beta), when the linear functions alpha(1), ... , alpha(m) define a normal crossing hyperplane configuration, and we use this to give a sufficient criterion on beta for the irreducibility of M-alpha(beta), in terms of numerical data for a resolution of the singularities of V(alpha).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 9. A concentration phenomenon for semilinear elliptic equations Ackermann, Nilset al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt594",{id:"formSmash:items:resultList:8:j_idt594",widgetVar:"widget_formSmash_items_resultList_8_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Szulkin, AndrzejStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A concentration phenomenon for semilinear elliptic equations2013In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 207, no 3, p. 1075-1089Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:8:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_8_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For a domain $\Omega\subset\dR^N$ we consider the equation $ -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $\Omega$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if $u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence $(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain $L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and $u_n$ are ground state solutions, then they concentrate at one of these points.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. CUTTING DOWN TREES WITH A MARKOV CHAINSAW Addario-Berry, Louigiet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt594",{id:"formSmash:items:resultList:9:j_idt594",widgetVar:"widget_formSmash_items_resultList_9_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Broutin, NicolasHolmgren, CeciliaStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); CUTTING DOWN TREES WITH A MARKOV CHAINSAW2014In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 24, no 6, p. 2297-2339Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:9:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_9_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton-Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny n. Our proof is based on a coupling which yields a precise, nonasymptotic distributional result for the case of uniformly random rooted labeled trees (or, equivalently, Poisson Galton-Watson trees conditioned on their size). Our approach also provides a new, random reversible transformation between Brownian excursion and Brownian bridge.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Hardy and spectral inequalities for a class of partial differential operators Aermark, Lior Alexandra PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt591",{id:"formSmash:items:resultList:10:j_idt591",widgetVar:"widget_formSmash_items_resultList_10_j_idt591",onLabel:"Aermark, Lior Alexandra ",offLabel:"Aermark, Lior Alexandra ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hardy and spectral inequalities for a class of partial differential operators2014Doctoral thesis, monograph (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:10:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_10_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This thesis is devoted to the study of Hardy and spectral inequalities for the Heisenberg and the Grushin operators. It consists of five chapters. In chapter 1 we present basic notions and summarize the main results of the thesis. In chapters 2-4 we deal with different types of Hardy inequalities for Laplace and Grushin operators with magnetic and non-magnetic fields. It was shown in an article by Laptev and Weidl that for some magnetic forms in two dimensions, the Hardy inequality holds in its classical form. More precisely, by considering the Aharonov-Bohm magnetic potential, we can improve the constant in the respective Hardy inequality. In chapter 2 we establish an L

^{p}- Hardy inequality related to Laplacians with magnetic fields with Aharonov-Bohm vector potentials. In chapter 3 we introduce a suitable notion of a vector field for the Grushin sub-elliptic operator G and obtain an improvement of the Hardy inequality, which was previously obtained in the paper of N. Garofallo and E. Lanconelli. In chapter 4 we find an L^{p}version of the Hardy inequality obtained in chapter 2. Finally in chapter 5 we aim to find the CLR and Lieb-Thirringbninequalities for harmonic Grushin-type operators. As the Grushin operator is non-elliptic, these inequalities will not take their classical form.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_10_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:10:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_10_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:10:j_idt854:0:fullText"});}); 12. Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field Aermark, Lior PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt591",{id:"formSmash:items:resultList:11:j_idt591",widgetVar:"widget_formSmash_items_resultList_11_j_idt591",onLabel:"Aermark, Lior ",offLabel:"Aermark, Lior ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt594",{id:"formSmash:items:resultList:11:j_idt594",widgetVar:"widget_formSmash_items_resultList_11_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Laptev, A.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field2012In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 23, no 2, p. 203-208Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:11:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_11_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A version of the Aharonov-Bohm magnetic field for a Grushin subelliptic operator is introduced; then its quadratic form is shown to satisfy an improved Hardy inequality.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. On the Modulus of Continuity of Mappings Between Euclidean Spaces Agbor, Dieudonnéet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt594",{id:"formSmash:items:resultList:12:j_idt594",widgetVar:"widget_formSmash_items_resultList_12_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Boman, JanStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the Modulus of Continuity of Mappings Between Euclidean Spaces2013In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 112, no 1, p. 147-160Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:12:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_12_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Let f be a function from R-P to R-q and let Lambda be a finite set of pairs (theta, eta) is an element of R-P x R-q. Assume that the real-valued function (eta, f(x)) is Lipschitz continuous in the direction theta for every (theta, eta) is an element of Lambda. Necessary and sufficient conditions on Lambda are given for this assumption to imply each of the following: (1) that f is Lipschitz continuous, and (2) that f is continuous with modulus of continuity <= C epsilon vertical bar log epsilon vertical bar.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. Persistence of embedded eigenvalues Agmon, Shmuelet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt594",{id:"formSmash:items:resultList:13:j_idt594",widgetVar:"widget_formSmash_items_resultList_13_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Herbst, IraMaad Sasane, SaraStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persistence of embedded eigenvalues2011In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 261, no 2, p. 451-477Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:13:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_13_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider conditions under. which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < infinity we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension in. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 15. A temporal perspective on the rate of convergence in first-passage percolation under a moment condition Ahlberg, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt591",{id:"formSmash:items:resultList:14:j_idt591",widgetVar:"widget_formSmash_items_resultList_14_j_idt591",onLabel:"Ahlberg, Daniel ",offLabel:"Ahlberg, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A temporal perspective on the rate of convergence in first-passage percolation under a moment condition2019In: Brazilian Journal of Probability and Statistics, ISSN 0103-0752, E-ISSN 2317-6199, Vol. 33, no 2, p. 397-401Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:14:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_14_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the rate of convergence in the celebrated Shape Theorem in first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are presented from a temporal perspective and complement previous work by the same author, in which the rate of convergence was studied from the standard spatial perspective.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. Noise sensitivity and Voronoi percolation Ahlberg, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt591",{id:"formSmash:items:resultList:15:j_idt591",widgetVar:"widget_formSmash_items_resultList_15_j_idt591",onLabel:"Ahlberg, Daniel ",offLabel:"Ahlberg, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt594",{id:"formSmash:items:resultList:15:j_idt594",widgetVar:"widget_formSmash_items_resultList_15_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Baldasso, RangelPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Noise sensitivity and Voronoi percolation2018In: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 23, article id 108Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:15:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_15_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we study noise sensitivity and threshold phenomena for Poisson Voronoi percolation on R-2. In the setting of Boolean functions, both threshold phenomena and noise sensitivity can be understood via the study of randomized algorithms. Together with a simple discretization argument, such techniques apply also to the continuum setting. Via the study of a suitable algorithm we show that box-crossing events in Voronoi percolation are noise sensitive and present a threshold phenomenon with polynomial window. We also study the effect of other kinds of perturbations, and emphasize the fact that the techniques we use apply for a broad range of models.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 17. Competing first passage percolation on random graphs with finite variance degrees Ahlberg, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt591",{id:"formSmash:items:resultList:16:j_idt591",widgetVar:"widget_formSmash_items_resultList_16_j_idt591",onLabel:"Ahlberg, Daniel ",offLabel:"Ahlberg, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt594",{id:"formSmash:items:resultList:16:j_idt594",widgetVar:"widget_formSmash_items_resultList_16_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Deijfen, MariaStockholm University, Faculty of Science, Department of Mathematics.Janson, SvantePrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Competing first passage percolation on random graphs with finite variance degrees2019In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, no 3, p. 545-559Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:16:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_16_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph in that an uninfected vertex becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of nearest neighbors of type 1 (2). Assuming (essentially) that the degree of a randomly chosen vertex has finite second moment, we show that if lambda(1) = lambda(2), then the fraction of vertices that are ultimately infected by type 1 converges to a continuous random variable V is an element of (0,1), as the number of vertices tends to infinity. Both infection types hence occupy a positive (random) fraction of the vertices. If lambda(1) not equal lambda(2), on the other hand, then the type with the larger intensity occupies all but a vanishing fraction of the vertices. Our results apply also to a uniformly chosen simple graph with the given degree sequence.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. Competition in growth and urns Ahlberg, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt591",{id:"formSmash:items:resultList:17:j_idt591",widgetVar:"widget_formSmash_items_resultList_17_j_idt591",onLabel:"Ahlberg, Daniel ",offLabel:"Ahlberg, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt594",{id:"formSmash:items:resultList:17:j_idt594",widgetVar:"widget_formSmash_items_resultList_17_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Griffiths, SimonJanson, SvanteMorris, RobertPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Competition in growth and urns2019In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 54, no 2, p. 211-227Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:17:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_17_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study survival among two competing types in two settings: a planar growth model related to two-neighbor bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncolored sites are given a color at rate 0, 1 or infinity, depending on whether they have zero, one, or at least two neighbors of that color. In the urn scheme, each vertex of a graph G has an associated urn containing some number of either blue or red balls ( but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system, a ball of the same color is added to each neighboring urn, and balls in the same urn but of different colors annihilate on a one-for-one basis. We show that, for every connected graph G and every initial configuration, only one color survives almost surely. As a corollary, we deduce that in the two-type growth model on Z(2), one of the colors only infects a finite number of sites with probability one. We also discuss generalizations to higher dimensions and multi-type processes, and list a number of open problems and conjectures.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:17:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 19. Existence of an unbounded vacant set for subcritical continuum percolation Ahlberg, Daniel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt591",{id:"formSmash:items:resultList:18:j_idt591",widgetVar:"widget_formSmash_items_resultList_18_j_idt591",onLabel:"Ahlberg, Daniel ",offLabel:"Ahlberg, Daniel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt594",{id:"formSmash:items:resultList:18:j_idt594",widgetVar:"widget_formSmash_items_resultList_18_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Tassion, VincentTeixeira, AugustoPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Existence of an unbounded vacant set for subcritical continuum percolation2018In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 23, article id 63Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:18:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_18_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider the Poisson Boolean percolation model in R-2, where the radius of each ball is independently chosen according to some probability measure with finite second moment. For this model, we show that the two thresholds, for the existence of an unbounded occupied and an unbounded vacant component, coincide. This complements a recent study of the sharpness of the phase transition in Poisson Boolean percolation by the same authors. As a corollary it follows that for Poisson Boolean percolation in R-d, for any d >= 2, finite moment of order d is both necessary and sufficient for the existence of a nontrivial phase transition for the vacant set.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:18:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 20. Displayed Categories Ahrens, Benediktet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt594",{id:"formSmash:items:resultList:19:j_idt594",widgetVar:"widget_formSmash_items_resultList_19_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lumsdaine, Peter LefanuStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Displayed Categories2019In: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 15, no 1, article id 20Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:19:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_19_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce and develop the notion of displayed categories. A displayed category over a category C is equivalent to 'a category D and functor F : D -> C', but instead of having a single collection of 'objects of D' with a map to the objects of C, the objects are given as a family indexed by objects of C, and similarly for the morphisms. This encapsulates a common way of building categories in practice, by starting with an existing category and adding extra data/properties to the objects and morphisms. The interest of this seemingly trivial reformulation is that various properties of functors are more naturally defined as properties of the corresponding displayed categories. Grothendieck fibrations, for example, when defined as certain functors, use equality on objects in their definition. When defined instead as certain displayed categories, no reference to equality on objects is required. Moreover, almost all examples of fibrations in nature are, in fact, categories whose standard construction can be seen as going via displayed categories. We therefore propose displayed categories as a basis for the development of fibrations in the type-theoretic setting, and similarly for various other notions whose classical definitions involve equality on objects. Besides giving a conceptual clarification of such issues, displayed categories also provide a powerful tool in computer formalisation, unifying and abstracting common constructions and proof techniques of category theory, and enabling modular reasoning about categories of multi-component structures. As such, most of the material of this article has been formalised in Coq over the UniMath library, with the aim of providing a practical library for use in further developments.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:19:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 21. CATEGORICAL STRUCTURES FOR TYPE THEORY IN UNIVALENT FOUNDATIONS Ahrens, Benediktet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt594",{id:"formSmash:items:resultList:20:j_idt594",widgetVar:"widget_formSmash_items_resultList_20_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lumsdaine, Peter LefanuStockholm University, Faculty of Science, Department of Mathematics.Voevodsky, VladimirPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); CATEGORICAL STRUCTURES FOR TYPE THEORY IN UNIVALENT FOUNDATIONS2018In: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 14, no 3, article id 18Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:20:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_20_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in univalent type theory, where the comparisons between them can be given more elementarily than in set-theoretic foundations. Specifically, we construct maps between the various types of structures, and show that assuming the Univalence axiom, some of the comparisons are equivalences. We then analyze how these structures transfer along (weak and strong) equivalences of categories, and, in particular, show how they descend from a category (not assumed univalent/saturated) to its Rezk completion. To this end, we introduce relative universes, generalizing the preceding notions, and study the transfer of such relative universes along suitable structure. We work throughout in (intensional) dependent type theory; some results, but not all, assume the univalence axiom. All the material of this paper has been formalized in Coq, over the UniMath library.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:20:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 22. MIRROR SYMMETRY AND THE CLASSIFICATION OF ORBIFOLD DEL PEZZO SURFACES Akhtar, Mohammadet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt594",{id:"formSmash:items:resultList:21:j_idt594",widgetVar:"widget_formSmash_items_resultList_21_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Coates, TomCorti, AlessioHeuberger, LianaKasprzyk, AlexanderOneto, AlessandroStockholm University, Faculty of Science, Department of Mathematics.Petracci, AndreaPrince, ThomasTveiten, KetilStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); MIRROR SYMMETRY AND THE CLASSIFICATION OF ORBIFOLD DEL PEZZO SURFACES2016In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 2, p. 513-527Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:21:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_21_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:21:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 23. The inductive wedge product of positive currents Al Abdulaali, Ahmad PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt591",{id:"formSmash:items:resultList:22:j_idt591",widgetVar:"widget_formSmash_items_resultList_22_j_idt591",onLabel:"Al Abdulaali, Ahmad ",offLabel:"Al Abdulaali, Ahmad ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The inductive wedge product of positive currentsManuscript (preprint) (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:22:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_22_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we discuss the wedge product of positive pluriharmonic (resp. plurisubharmonic) current of bidimension $(p,p)$ with the Monge-Ampère operator of plurisubharmonic function. In the first part of the paper, we define this product when the locus points of the plurisubharmonic function are located in a (2p-2)-dimensional closed set (resp. (2p-4)-dimensional sets), in the sense of Hartogs. The second part treats the case when these locus points are contained in a compact complete pluripolar sets and p≥ 2 (resp. p≥3).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:22:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 24. On the Extension and Wedge Product of Positive Currents Al Abdulaali, Ahmad Khalid PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt591",{id:"formSmash:items:resultList:23:j_idt591",widgetVar:"widget_formSmash_items_resultList_23_j_idt591",onLabel:"Al Abdulaali, Ahmad Khalid ",offLabel:"Al Abdulaali, Ahmad Khalid ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the Extension and Wedge Product of Positive Currents2012Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:23:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_23_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This dissertation is concerned with extensions and wedge products of positive currents. Our study can be considered as a generalization for classical works done earlier in this field.

Paper I deals with the extension of positive currents across different types of sets. For closed complete pluripolar obstacles, we show the existence of such extensions. To do so, further Hausdorff dimension conditions are required. Moreover, we study the case when these obstacles are zero sets of strictly

*k*-convex functions.In Paper II, we discuss the wedge product of positive pluriharmonic (resp. plurisubharmonic) current of bidimension

*(p,p)*with the Monge-Ampère operator of plurisubharmonic function. In the first part of the paper, we define this product when the locus points of the plurisubharmonic function are located in a*(2p-2)*-dimensional closed set (resp.*(2p-4)*-dimensional sets), in the sense of Hartogs. The second part treats the case when these locus points are contained in a compact complete pluripolar sets and*p≥2*(resp.*p≥3*).Paper III studies the extendability of negative

*S*-plurisubharmonic current of bidimension*(p,p)*across a*(2p-2)*-dimensional closed set. Using only the positivity of S, we show that such extensions exist in the case when these obstacles are complete pluripolar, as well as zero sets of*C*^{2}-plurisubharmoinc functions.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:23:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_23_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:23:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_23_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:23:j_idt854:0:fullText"});}); 25. Embedding Small Digraphs and Permutations in Binary Trees and Split Trees Albert, Michaelet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt594",{id:"formSmash:items:resultList:24:j_idt594",widgetVar:"widget_formSmash_items_resultList_24_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Holmgren, CeciliaJohansson, TonyStockholm University, Faculty of Science, Department of Mathematics.Skerman, FionaPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Embedding Small Digraphs and Permutations in Binary Trees and Split Trees2020In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 82, no 3, p. 589-615Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:24:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_24_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees (Cai et al. in Combin Probab Comput 28(3):335-364, 2019). We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye (SIAM J Comput 28(2):409-432, 1998. 10.1137/s0097539795283954). Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree, with probability tending to one as the number of balls increases, the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embeddings of digraphs into split trees which may be of independent interest.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:24:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 26. Singular perturbations of differential operators Albeverio, Sergioet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt594",{id:"formSmash:items:resultList:25:j_idt594",widgetVar:"widget_formSmash_items_resultList_25_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kurasov, PavelStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Singular perturbations of differential operators: solvable Schrödinger type operators2000Book (Refereed)27. Combinatorial Methods in Complex Analysis Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt591",{id:"formSmash:items:resultList:26:j_idt591",widgetVar:"widget_formSmash_items_resultList_26_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Combinatorial Methods in Complex Analysis2013Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:26:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_26_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The theme of this thesis is combinatorics, complex analysis and algebraic geometry. The thesis consists of six articles divided into four parts.

**Part A:***Spectral properties of the Schrödinger equation*This part consists of Papers I-II, where we study a univariate Schrödinger equation with a complex polynomial potential. We prove that the set of polynomial potentials that admit solutions to the Schrödingerequation is connected, under certain boundary conditions. We also study a similar result for even polynomial potentials, where a similar result is obtained.

**Part B:***Graph monomials and sums of squares*In this part, consisting of Paper III, we study natural bases for the space of homogeneous, symmetric and translation-invariant polynomials in terms of multigraphs. We find all multigraphs with at most six edges that give rise to non-negative polynomials, and which of these that can be expressed as a sum of squares. Such polynomials appear naturally in connection to expressing certain non-negative polynomials as sums of squares.

**Part C:***Eigenvalue asymptotics of banded Toeplitz matrices*This part consists of Papers IV-V. We give a new and generalized proof of a theorem by P. Schmidt and F. Spitzer concerning asymptotics of eigenvalues of Toeplitz matrices. We also generalize the notion of eigenvalues to rectangular matrices, and partially prove the a multivariate analogue of the above.

**Part D:***Stretched Schur polynomials*This part consists of Paper VI, where we give a combinatorial proof that certain sequences of skew Schur polynomials satisfy linear recurrences with polynomial coefficients.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:26:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)Fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_26_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:26:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_26_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:26:j_idt854:0:fullText"});}); 28. LLT polynomials, elementary symmetric functions and melting lollipops Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt591",{id:"formSmash:items:resultList:27:j_idt591",widgetVar:"widget_formSmash_items_resultList_27_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); LLT polynomials, elementary symmetric functions and melting lollipops2020In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:27:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_27_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We conjecture an explicit positive combinatorial formula for the expansion of unicellular LLT polynomials in the elementary symmetric basis. This is an analogue of the Shareshian-Wachs conjecture previously studied by Panova and the author in 2018. We show that the conjecture for unicellular LLT polynomials implies a similar formula for vertical-strip LLT polynomials. We prove positivity in the elementary symmetric basis for the class of graphs called melting lollipops previously considered by Huh, Nam and Yoo. This is done by proving a curious relationship between a generalization of charge and orientations of unit-interval graphs. We also provide short bijective proofs of Lee's three-term recurrences for unicellular LLT polynomials, and we show that these recurrences are enough to generate all unicellular LLT polynomials associated with abelian area sequences.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:27:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 29. On Eigenvalues of the Schrodinger Operator with an Even Complex-Valued Polynomial Potential Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt591",{id:"formSmash:items:resultList:28:j_idt591",widgetVar:"widget_formSmash_items_resultList_28_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On Eigenvalues of the Schrodinger Operator with an Even Complex-Valued Polynomial Potential2012In: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 12, no 2, p. 465-481Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:28:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_28_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we generalize several results in the article Analytic continuation of eigenvalues of a quartic oscillator of A. Eremenko and A. Gabrielov [4]. We consider a family of eigenvalue problems for a Schrodinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k < (d + 2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively. In the case with k = (d + 2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:28:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 30. On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt591",{id:"formSmash:items:resultList:29:j_idt591",widgetVar:"widget_formSmash_items_resultList_29_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential2010Licentiate thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:29:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_29_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials.

In the first paper, we consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.

In the second paper, we only consider even polynomial potentials, and show that the spectral determinant for the eigenvalue problem consists of two irreducible components. A similar result to that of paper I is proved for k boundary conditions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:29:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_29_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:29:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_29_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:29:j_idt854:0:fullText"});}); 31. Schur polynomials, banded Toeplitz matrices and Widom's formula Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt591",{id:"formSmash:items:resultList:30:j_idt591",widgetVar:"widget_formSmash_items_resultList_30_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Schur polynomials, banded Toeplitz matrices and Widom's formula2012In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 19, no 4, p. P22-Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:30:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_30_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We prove that for arbitrary partitions lambda subset of kappa, and integers 0 <= c < r <= n, the sequence of Schur polynomials S(kappa+k.1c)/(lambda+k.1r)(x(1), ... , x(n)) for k sufficiently large, satisfy a linear recurrence. The roots of the characteristic equation are given explicitly. These recurrences are also valid for certain sequences of minors of banded Toeplitz matrices. In addition, we show that Widom's determinant formula from 1958 is a special case of a well-known identity for Schur polynomials.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:30:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)Fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_30_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:30:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_30_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:30:j_idt854:0:fullText"});}); 32. Stretched skew Schur polynomials are recurrent Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt591",{id:"formSmash:items:resultList:31:j_idt591",widgetVar:"widget_formSmash_items_resultList_31_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stretched skew Schur polynomials are recurrent2014In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 122, p. 1-8Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:31:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_31_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We show that sequences of skew Schur polynomials obtained from stretched semi-standard Young tableauxsatisfy a linear recurrence, which we give explicitly.Using this, we apply this to finding certain asymptotic behavior of these Schur polynomials and present conjectures on minimal recurrences for stretched Schur polynomials.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:31:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 33. On Eigenvalues of the Schrödinger Operator with a Complex-Valued Polynomial Potential Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt591",{id:"formSmash:items:resultList:32:j_idt591",widgetVar:"widget_formSmash_items_resultList_32_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt594",{id:"formSmash:items:resultList:32:j_idt594",widgetVar:"widget_formSmash_items_resultList_32_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Gabrielov, AndreiPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On Eigenvalues of the Schrödinger Operator with a Complex-Valued Polynomial Potential2012In: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 12, no 1, p. 119-144Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:32:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_32_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree

*d*and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation.We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying

*k*> 2 boundary conditions, except for the case*d*is even and*k*=*d*/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.The first results can be derived from H. Habsch, while the case of a disconnected parameter space is new.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:32:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 34. The cyclic sieving phenomenon on circular Dyck paths Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt591",{id:"formSmash:items:resultList:33:j_idt591",widgetVar:"widget_formSmash_items_resultList_33_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt594",{id:"formSmash:items:resultList:33:j_idt594",widgetVar:"widget_formSmash_items_resultList_33_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Linusson, SvantePotka, SamuPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The cyclic sieving phenomenon on circular Dyck paths2019In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 26, no 4, article id P4.16Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:33:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_33_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We give a

*q*-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this*q*-analogue exhibits the cyclic sieving phenomenon under a natural action of the cyclic group. The enumeration and cyclic sieving is generalized to Mobius paths. We also discuss properties of a generalization of cyclic sieving, which we call*subset cyclic sieving*, and introduce the notion of*Lyndon-like cyclic sieving*that concerns special recursive properties of combinatorial objects exhibiting the cyclic sieving phenomenon.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:33:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 35. Around multivariate Schmidt-Spitzer theorem Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt591",{id:"formSmash:items:resultList:34:j_idt591",widgetVar:"widget_formSmash_items_resultList_34_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt594",{id:"formSmash:items:resultList:34:j_idt594",widgetVar:"widget_formSmash_items_resultList_34_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Shapiro, BorisStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Around multivariate Schmidt-Spitzer theorem2014In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 446, p. 356-368Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:34:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_34_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Given an arbitrary complex-valued infinite matrix $\infmatA=(a_{ij}),$$i=1,\dotsc,\infty;$ $j=1,\dotsc,\infty$ and a positive integer $n$ we introduce anaturally associated polynomial basis $\polybasis_\infmatA$ of$\C[x_0,\dotsc,x_n]$.We discuss some properties of the locus of common zeros of all polynomials in $\polybasis_A$ having a given degree $m$; the latter locus can beinterpreted as the spectrum of the $m\times (m+n)$-submatrix of $\infmatA$ formed by its $m$ first rows and$(m+n)$ first columns. We initiate the study of the asymptotics of these spectra when $m\to \infty$ inthe case when $\infmatA$ is a banded Toeplitz matrix.In particular, we present and partially prove a conjectural multivariate analogof the well-known Schmidt-Spitzer theorem which describes the spectral asymptotics for the sequence of principal minors of an arbitrarybanded Toeplitz matrix.Finally, we discuss relations between polynomial bases $\polybasis_\infmatA$ andmultivariate orthogonal polynomials.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:34:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_34_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:34:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_34_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:34:j_idt854:0:fullText"});}); 36. Discriminants, Symmetrized Graph monomials and Sums of Squares Alexandersson, Per PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt591",{id:"formSmash:items:resultList:35:j_idt591",widgetVar:"widget_formSmash_items_resultList_35_j_idt591",onLabel:"Alexandersson, Per ",offLabel:"Alexandersson, Per ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt594",{id:"formSmash:items:resultList:35:j_idt594",widgetVar:"widget_formSmash_items_resultList_35_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Shapiro, BorisStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Discriminants, Symmetrized Graph monomials and Sums of Squares2012In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 21, no 4, p. 353-361Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:35:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_35_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In 1878, motivated by the requirements of the invariant the-ory of binary forms, J. J. Sylvester constructed, for every graphwith possible multiple edges but without loops, its symmetrizedgraph monomial, which is a polynomial in the vertex labels ofthe original graph. We pose the question for which graphs thispolynomial is nonnegative or a sum of squares. This problem ismotivated by a recent conjecture of F. Sottile and E. Mukhin onthe discriminant of the derivative of a univariate polynomial andby an interesting example of P. and A. Lax of a graph with fouredges whose symmetrized graph monomial is nonnegative butnot a sum of squares. We present detailed information about sym-metrized graph monomials for graphs with four and six edges,obtained by computer calculations.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:35:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 37. Modeling Realized Covariance of Asset Returns Alfelt, Gustav PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt591",{id:"formSmash:items:resultList:36:j_idt591",widgetVar:"widget_formSmash_items_resultList_36_j_idt591",onLabel:"Alfelt, Gustav ",offLabel:"Alfelt, Gustav ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Modeling Realized Covariance of Asset Returns2019Licentiate thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:36:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_36_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis, which consists of two papers, we consider the modeling of positive definitive symmetric matrices, in particular covariance matrices of financial asset returns. The return covariance matrix describes the magnitude in which prices of financial assets tend to change over time, and how price changes between different assets are related. It is an instrumental quantity in many financial applications, and furthermore, an important component in understanding the dynamics present prior to and during times of financial turbulence, such as the 2008 financial crisis.

In the first paper, we provide several goodness-of-fit tests applicable to models driven by a centralized Wishart process. To apply such a distributional assumption has become a popular way of modeling the stochastic properties of time-series of realized covariance matrices for asset returns. The paper includes a simulation study that aims to investigate how the tests perform under model uncertainty stemming from parameter estimation. In addition, the presented methods are used to evaluate the fit of a typical model of realized covariance adapted to real data on six stocks traded on the New York Stock Exchange.

The second paper considers positive definite and symmetric random matrices of the exponential family. Under certain conditions for this class of distributions, we derive the Stein-Haff identity. Furthermore, we determine this identity in the case of the matrix-variate gamma distribution and apply it in order to present an estimator that outperforms the maximum likelihood estimator in terms of Stein's loss function. Finally, a small simulation study is conducted to support the theoretical results.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:36:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 38. Stein-Haff Identity for the Exponential Family Alfelt, Gustav PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt591",{id:"formSmash:items:resultList:37:j_idt591",widgetVar:"widget_formSmash_items_resultList_37_j_idt591",onLabel:"Alfelt, Gustav ",offLabel:"Alfelt, Gustav ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stein-Haff Identity for the Exponential Family2018In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 99, p. 7-18Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:37:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_37_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, the Stein-Haff identity is established for positive-definite and symmetric random matrices belonging to the exponential family. The identity is then applied to the matrix-variate gamma distribution, and an estimator that dominates the maximum likelihood estimator in terms of Stein's loss is obtained. Finally, a simulation study is conducted in order to support the theoretical results.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:37:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 39. Goodness-of-fit tests for centralized Wishart processes Alfelt, Gustav PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt591",{id:"formSmash:items:resultList:38:j_idt591",widgetVar:"widget_formSmash_items_resultList_38_j_idt591",onLabel:"Alfelt, Gustav ",offLabel:"Alfelt, Gustav ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt594",{id:"formSmash:items:resultList:38:j_idt594",widgetVar:"widget_formSmash_items_resultList_38_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Bodnar, TarasStockholm University, Faculty of Science, Department of Mathematics.Tyrcha, JoannaStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Goodness-of-fit tests for centralized Wishart processes2019In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:38:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_38_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we present several goodness-of-fit tests for the centralized Wishart process, a popular matrix-variate time series model used to capture the stochastic properties of realized covariance matrices. The new test procedures are based on the extended Bartlett decomposition derived from the properties of the Wishart distribution and allows to obtain sets of independently and standard normally distributed random variables under the null hypothesis. Several tests for normality and independence are then applied to these variables in order to support or to reject the underlying assumption of a centralized Wishart process. In order to investigate the influence of estimated parameters on the suggested testing procedures in the finite-sample case, a simulation study is conducted. Finally, the new test methods are applied to real data consisting of realized covariance matrices computed for the returns on six assets traded on the New York Stock Exchange.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:38:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 40. Scan Statistics for Space-Time Cluster Detection Allévius, Benjamin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt591",{id:"formSmash:items:resultList:39:j_idt591",widgetVar:"widget_formSmash_items_resultList_39_j_idt591",onLabel:"Allévius, Benjamin ",offLabel:"Allévius, Benjamin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Scan Statistics for Space-Time Cluster Detection2018Licentiate thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:39:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_39_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Scan statistics are used by public health agencies to detect and localize disease outbreaks. This thesis provides an overview of scan statistics in the context of prospective disease surveillance and outbreak detection, presents a novel scan statistic to deal with the type of zero-abundant data that is often encountered in these settings, and—perhaps most importantly—implements this and other scan statistics in a freely available and open source R package. Additionally, Markov processes and time series methods are frequently used in many disease surveillance methods. The last part of this thesis presents some computationally efficient methods for density evaluation and simulation of irregularly sampled AR(1) processes, that may be useful when implementing surveillance methods based on these types of processes.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:39:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 41. An unconditional space–time scan statistic for ZIP‐distributed data Allévius, Benjamin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt591",{id:"formSmash:items:resultList:40:j_idt591",widgetVar:"widget_formSmash_items_resultList_40_j_idt591",onLabel:"Allévius, Benjamin ",offLabel:"Allévius, Benjamin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt594",{id:"formSmash:items:resultList:40:j_idt594",widgetVar:"widget_formSmash_items_resultList_40_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Höhle, MichaelStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); An unconditional space–time scan statistic for ZIP‐distributed data2019In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 46, no 1, p. 142-159Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:40:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_40_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A scan statistic is proposed for the prospective monitoring of spatiotemporal count data with an excess of zeros. The method that is based on an outbreak model for the zero‐inflated Poisson distribution is shown to be superior to traditional scan statistics based on the Poisson distribution in the presence of structural zeros. The spatial accuracy and the detection timeliness of the proposed scan statistic are investigated by means of simulation, and an application on the weekly cases of Campylobacteriosis in Germany illustrates how the scan statistic could be used to detect emerging disease outbreaks. An implementation of the method is provided in the open‐source R package scanstatistics available on the Comprehensive R Archive Network.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:40:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_40_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:40:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_40_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:40:j_idt854:0:fullText"});}); 42. A Universal A(infinity) Structure on BV Algebras with Multiple Zeta Value Coefficients Alm, Johan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt591",{id:"formSmash:items:resultList:41:j_idt591",widgetVar:"widget_formSmash_items_resultList_41_j_idt591",onLabel:"Alm, Johan ",offLabel:"Alm, Johan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Universal A(infinity) Structure on BV Algebras with Multiple Zeta Value Coefficients2016In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 24, p. 7414-7470Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:41:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_41_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We construct an explicit and universal A-infinity deformation of Batalin-Vilkovisky algebras, with all coefficients expressed as rational sums of multiple zeta values. If the Batalin-Vilkovisky algebra that we start with is cyclic, then so is the A-infinity deformation. Moreover, the adjoint action of the odd Poisson bracket acts by derivations of the A-infinity structure. The construction conjecturally defines a new presentation of the Grothendieck-Teichmuller Lie algebra.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:41:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 43. Universal algebraic structures on polyvector fields Alm, Johan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt591",{id:"formSmash:items:resultList:42:j_idt591",widgetVar:"widget_formSmash_items_resultList_42_j_idt591",onLabel:"Alm, Johan ",offLabel:"Alm, Johan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Universal algebraic structures on polyvector fields2014Doctoral thesis, monograph (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:42:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_42_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The theory of operads is a conceptual framework that has become a kind of universal language, relating branches of topology and algebra. This thesis uses the operadic framework to study the derived algebraic properties of polyvector fields on manifolds.The thesis is divided into eight chapters. The first is an introduction to the thesis and the research field to which it belongs, while the second chapter surveys the basic mathematical results of the field.The third chapter is devoted to a novel construction of differential graded operads, generalizing an earlier construction due to Thomas Willwacher. The construction highlights and explains several categorical properties of differential graded algebras (of some kind) that come equipped with an action by a differential graded Lie algebra. In particular, the construction clarifies the deformation theory of such algebras and explains how such algebras can be twisted by Maurer-Cartan elements.The fourth chapter constructs an explicit strong homotopy deformation of polynomial polyvector fields on affine space, regarded as a two-colored noncommutative Gerstenhaber algebra. It also constructs an explicit strong homotopy quasi-isomorphism from this deformation to the canonical two-colored noncommmutative Gerstenhaber algebra of polydifferential operators on the affine space. This explicit construction generalizes Maxim Kontsevich's formality morphism.The main result of the fifth chapter is that the deformation of polyvector fields constructed in the fourth chapter is (generically) nontrivial and, in a sense, the unique such deformation. The proof is based on some cohomology computations involving Kontsevich's graph complex and related complexes. The chapter ends with an application of the results to properties of a derived version of the Duflo isomorphism.The sixth chapter develops a general mathematical framework for how and when an algebraic structure on the germs at the origin of a sheaf on Cartesian space can be "globalized" to a corresponding algebraic structure on the global sections over an arbitrary smooth manifold. The results are applied to the construction of the fourth chapter, and it is shown that the construction globalizes to polyvector fields and polydifferential operators on an arbitrary smooth manifold.The seventh chapter combines the relations to graph complexes, explained in chapter five, and the globalization theory of chapter six, to uncover a representation of the Grothendieck-Teichmüller group in terms of A-infinity morphisms between Poisson cohomology cochain complexes on a manifold.Chapter eight gives a simplified version of a construction of a family of Drinfel'd associators due to Carlo Rossi and Thomas Willwacher. Our simplified construction makes the connections to multiple zeta values more transparent--in particular, one obtains a fairly explicit family of evaluations on the algebra of formal multiple zeta values, and the chapter proves certain basic properties of this family of evaluations.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:42:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)almthesis$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_42_j_idt854_0_j_idt857",{id:"formSmash:items:resultList:42:j_idt854:0:j_idt857",widgetVar:"widget_formSmash_items_resultList_42_j_idt854_0_j_idt857",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:42:j_idt854:0:fullText"});}); 44. Grothendieck-Teichmuller group and Poisson cohomologies Alm, Johan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt591",{id:"formSmash:items:resultList:43:j_idt591",widgetVar:"widget_formSmash_items_resultList_43_j_idt591",onLabel:"Alm, Johan ",offLabel:"Alm, Johan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt594",{id:"formSmash:items:resultList:43:j_idt594",widgetVar:"widget_formSmash_items_resultList_43_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Merkulov, SergeiStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Grothendieck-Teichmuller group and Poisson cohomologies2015In: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 9, no 1, p. 185-214Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:43:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_43_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study actions of the Grothendieck-Teichmuller group GRT on Poisson cohomologies of Poisson manifolds, and prove some go and no-go theorems associated with these actions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:43:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 45. Brown's dihedral moduli space and freedom of the gravity operad Alm, Johan PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt591",{id:"formSmash:items:resultList:44:j_idt591",widgetVar:"widget_formSmash_items_resultList_44_j_idt591",onLabel:"Alm, Johan ",offLabel:"Alm, Johan ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt594",{id:"formSmash:items:resultList:44:j_idt594",widgetVar:"widget_formSmash_items_resultList_44_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Petersen, DanPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Brown's dihedral moduli space and freedom of the gravity operad2017In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 50, no 5, p. 1081-1122Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:44:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_44_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Francis Brown introduced a partial compactification M-0,n(delta) of the moduli space M-0,M-n. We prove that the gravity cooperad, given by the degree-shifted cohomologies of the spaces M-0,M-n, is cofree as a nonsymmetric anticyclic cooperad; moreover, the cogenerators are given by the cohomology groups of M-0,n(delta). As part of the proof we construct an explicit diagrammatically defined basis of H.(M-0,M-n) which is compatible with cooperadic cocomposition, and such that a subset forms a basis of H.(M-0,n(delta)). We show that our results are equivalent to the claim that H-k (M-0,n(delta)) has a pure Hodge structure of weight 2k for all k, and we conclude our paper by giving an independent and completely different proof of this fact. The latter proof uses a new and explicit iterative construction of M-0,n(delta) from A(n-3) by blow-ups and removing divisors, analogous to Kapranov's and Keel's constructions of (M) over bar (0,n) from Pn-3 and (P-1)(n-3), respectively.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:44:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 46. Valuation of Index-Linked Cash Flows in a Heath-Jarrow-Morton Framework Alm, Jonaset al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt594",{id:"formSmash:items:resultList:45:j_idt594",widgetVar:"widget_formSmash_items_resultList_45_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lindskog, FilipStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Valuation of Index-Linked Cash Flows in a Heath-Jarrow-Morton Framework2015In: Risks, ISSN 1670-0139, E-ISSN 2227-9091, Vol. 3, no 3, p. 338-364Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:45:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_45_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath-Jarrow-Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:45:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 47. Stokastik Alm, Sven Ericket al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt594",{id:"formSmash:items:resultList:46:j_idt594",widgetVar:"widget_formSmash_items_resultList_46_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Britton, TomStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stokastik2008Book (Other (popular science, discussion, etc.))48. First Passage Percolation on \(\mathbb {Z}^2\) Alm, Sven Ericket al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt594",{id:"formSmash:items:resultList:47:j_idt594",widgetVar:"widget_formSmash_items_resultList_47_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Deijfen, MariaStockholm University, Faculty of Science, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); First Passage Percolation on \(\mathbb {Z}^2\): A Simulation Study2015In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, no 3, p. 657-678Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:47:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_47_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:47:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 49. LifeGene-a large prospective population-based study of global relevance Almqvist, Catarinaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt594",{id:"formSmash:items:resultList:48:j_idt594",widgetVar:"widget_formSmash_items_resultList_48_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Adami, Hans-OlovFranks, Paul W.Groop, LeifIngelsson, ErikKere, JuhaLissner, LaurenLitton, Jan-EricMaeurer, MarkusMichaelsson, KarlPalmgren, JuniStockholm University, Faculty of Science, Department of Mathematics.Pershagen, GoranPloner, AlexanderSullivan, Patrick F.Tybring, GunnelPedersen, Nancy L.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); LifeGene-a large prospective population-based study of global relevance2011In: European Journal of Epidemiology, ISSN 0393-2990, E-ISSN 1573-7284, Vol. 26, no 1, p. 67-77Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:48:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_48_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Studying gene-environment interactions requires that the amount and quality of the lifestyle data is comparable to what is available for the corresponding genomic data. Sweden has several crucial prerequisites for comprehensive longitudinal biomedical research, such as the personal identity number, the universally available national health care system, continuously updated population and health registries and a scientifically motivated population. LifeGene builds on these strengths to bridge the gap between basic research and clinical applications with particular attention to populations, through a unique design in a research-friendly setting. LifeGene is designed both as a prospective cohort study and an infrastructure with repeated contacts of study participants approximately every 5 years. Index persons aged 18-45 years old will be recruited and invited to include their household members (partner and any children). A comprehensive questionnaire addressing cutting-edge research questions will be administered through the web with short follow-ups annually. Biosamples and physical measurements will also be collected at baseline, and re-administered every 5 years thereafter. Event-based sampling will be a key feature of LifeGene. The household-based design will give the opportunity to involve young couples prior to and during pregnancy, allowing for the first study of children born into cohort with complete pre-and perinatal data from both the mother and father. Questions and sampling schemes will be tailored to the participants' age and life events. The target of LifeGene is to enrol 500,000 Swedes and follow them longitudinally for at least 20 years.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:48:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 50. Can we measure the difficulty of an optimization problem? Alpcan, Tansuet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt594",{id:"formSmash:items:resultList:49:j_idt594",widgetVar:"widget_formSmash_items_resultList_49_j_idt594",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Everitt, TomStockholm University, Faculty of Science, Department of Mathematics.Hutter, MarcusPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Can we measure the difficulty of an optimization problem?2014Conference paper (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt629_0_j_idt630",{id:"formSmash:items:resultList:49:j_idt629:0:j_idt630",widgetVar:"widget_formSmash_items_resultList_49_j_idt629_0_j_idt630",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Can we measure the difficulty of an optimization problem? Although optimization plays a crucial role in modernscience and technology, a formal framework that puts problemsand solution algorithms into a broader context has not beenestablished. This paper presents a conceptual approach which gives a positive answer to the question for a broad class of optimization problems. Adopting an information and computational perspective, the proposed framework builds upon Shannon and algorithmic information theories. As a starting point, a concrete model and definition of optimization problems is provided. Then, a formal definition of optimization difficulty is introduced which builds upon algorithmic information theory. Following an initial analysis, lower and upper bounds on optimization difficulty are established. One of the upper-bounds is closely related to Shannon information theory and black-box optimization. Finally, various computational issues and future research directions are discussed.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:49:j_idt629:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500});

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http://www.diva-portal.org/smash/resultList.jsf?query=&language=en&searchType=SIMPLE&noOfRows=50&sortOrder=author_sort_asc&sortOrder2=title_sort_asc&onlyFullText=false&sf=all&aq=%5B%5B%7B%22organisationId%22%3A%22620%22%7D%5D%5D&aqe=%5B%5D&aq2=%5B%5B%5D%5D&af=%5B%5D $(function(){PrimeFaces.cw("InputTextarea","widget_formSmash_lower_j_idt911_recordPermLink",{id:"formSmash:lower:j_idt911:recordPermLink",widgetVar:"widget_formSmash_lower_j_idt911_recordPermLink",autoResize:true});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt911_j_idt913",{id:"formSmash:lower:j_idt911:j_idt913",widgetVar:"widget_formSmash_lower_j_idt911_j_idt913",target:"formSmash:lower:j_idt911:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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Cite

Citation styleapa ieee modern-language-association-8th-edition vancouver Other style $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt929",{id:"formSmash:lower:j_idt929",widgetVar:"widget_formSmash_lower_j_idt929",behaviors:{change:function(ext) {PrimeFaces.ab({s:"formSmash:lower:j_idt929",e:"change",f:"formSmash",p:"formSmash:lower:j_idt929",u:"formSmash:lower:otherStyle"},ext);}}});});

- apa
- ieee
- modern-language-association-8th-edition
- vancouver
- Other style

Languagede-DE en-GB en-US fi-FI nn-NO nn-NB sv-SE Other locale $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt940",{id:"formSmash:lower:j_idt940",widgetVar:"widget_formSmash_lower_j_idt940",behaviors:{change:function(ext) {PrimeFaces.ab({s:"formSmash:lower:j_idt940",e:"change",f:"formSmash",p:"formSmash:lower:j_idt940",u:"formSmash:lower:otherLanguage"},ext);}}});});

- de-DE
- en-GB
- en-US
- fi-FI
- nn-NO
- nn-NB
- sv-SE
- Other locale

Output formathtml text asciidoc rtf $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt950",{id:"formSmash:lower:j_idt950",widgetVar:"widget_formSmash_lower_j_idt950"});});

- html
- text
- asciidoc
- rtf