CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt165",{id:"formSmash:upper:j_idt165",widgetVar:"widget_formSmash_upper_j_idt165",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt166_j_idt168",{id:"formSmash:upper:j_idt166:j_idt168",widgetVar:"widget_formSmash_upper_j_idt166_j_idt168",target:"formSmash:upper:j_idt166:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Period integrals and other direct images of D-modulesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Department of Mathematics, Stockholm University , 2015. , 32 p.
##### Keyword [en]

D-modules, Rings of differential operators, Period integrals
##### National Category

Algebra and Logic
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-116790ISBN: 978-91-7649-182-9 (print)OAI: oai:DiVA.org:su-116790DiVA: diva2:808420
##### Public defence

2015-09-18, sal 14, hus 5 Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt482",{id:"formSmash:j_idt482",widgetVar:"widget_formSmash_j_idt482",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt488",{id:"formSmash:j_idt488",widgetVar:"widget_formSmash_j_idt488",multiple:true});
##### Note

##### List of papers

This thesis consists of three papers, each touching on a different aspect of the theory of rings of differential operators and *D*-modules. In particular, an aim is to provide and make explicit good examples of *D*-module directimages, which are all but absent in the existing literature.The first paper makes explicit the fact that *B-splines* (a particular class of piecewise polynomial functions) are solutions to *D*-module theoretic direct images of a class of *D*-modules constructed from polytopes.These modules, and their direct images, inherit all the relevant combinatorial structure from the defining polytopes, and as such are extremely well-behaved.The second paper studies the ring of differential operator on a reduced monomial ring (aka. *Stanley-Reisner* ring), in arbitrary characteristic.The two-sided ideal structure of the ring of differential operators is described in terms of the associated abstract simplicial complex, and several quite different proofs are given.The third paper computes the monodromy of the period integrals of Laurent polynomials about the singular point at the origin. The monodromy is describable in terms of the Newton polytope of the Laurent polynomial, in particular the combinatorial-algebraic operation of *mutation* plays an important role. Special attention is given to the class of *maximally mutable* Laurent polynomials, as these are one side of the conjectured correspondance that classifies Fano manifolds via mirror symmetry.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Accepted. Paper 2: Manuscript. Paper 3: Manuscript.

Available from: 2015-08-26 Created: 2015-04-27 Last updated: 2016-10-19Bibliographically approved1. B-splines, polytopes and their characteristic D-modules$(function(){PrimeFaces.cw("OverlayPanel","overlay808333",{id:"formSmash:j_idt524:0:j_idt530",widgetVar:"overlay808333",target:"formSmash:j_idt524:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Two-sided ideals in the ring of differential operators on a Stanley-Reisner ring$(function(){PrimeFaces.cw("OverlayPanel","overlay808334",{id:"formSmash:j_idt524:1:j_idt530",widgetVar:"overlay808334",target:"formSmash:j_idt524:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Period integrals and mutation$(function(){PrimeFaces.cw("OverlayPanel","overlay808335",{id:"formSmash:j_idt524:2:j_idt530",widgetVar:"overlay808335",target:"formSmash:j_idt524:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});