{"id":3648,"date":"2023-09-08T15:56:47","date_gmt":"2023-09-08T13:56:47","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/blog\/research-groups\/pieter-belmans-research-group\/research\/"},"modified":"2026-04-24T15:02:13","modified_gmt":"2026-04-24T13:02:13","slug":"research","status":"publish","type":"research-groups","link":"https:\/\/www.uni.lu\/fstm-en\/research-groups\/geometry-through-categories-and-noncommutative-algebra\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<div class=\"section py-0 static\">\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><!-- SecondaryNavigationMirror --><div class=\"js-secondary-nav--sticky wp-block-unilux-blocks-secondary-navigation\" id=\"af06cf4a-2f16-4afb-8a26-4496ef22080b\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button class=\"secondary-nav__button btn btn-solid--primary w-full\" aria-expanded=\"false\" aria-controls=\"secondary-navigation__list\" title=\"The selected page is Overview\" type=\"button\">\n            <span class=\"btn__name mr-auto\">Overview<\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n            <\/svg>\n        <\/button>\n\n        <ul id=\"secondary-navigation__list\" class=\"secondary-nav__list\">\n            <li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/geometry-through-categories-and-noncommutative-algebra\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Overview<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/geometry-through-categories-and-noncommutative-algebra\/research\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link isactived\" aria-current=\"page\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Research<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/geometry-through-categories-and-noncommutative-algebra\/people\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">People<\/span>\n    <\/a>\n<\/li>\n        <\/ul>\n    <\/nav>\n<\/div>\n<!-- end SecondaryNavigationMirror --><\/div><\/section>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h1 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"geometry-through-categories-and-noncommutative-algebra\"\n    >\nGeometry through categories and noncommutative algebra<\/h1>\n\n\n\n<p>Our research group&nbsp;studies&nbsp;algebraic varieties and noncommutative algebras, and their invariants,&nbsp;usually&nbsp;with an emphasis on&nbsp;Fano varieties or&nbsp;moduli spaces of sheaves and representations.&nbsp;We&nbsp;often&nbsp;do this&nbsp;through the point-of-view of derived categories, with the goal of understanding their deformation theory, or understanding aspects of (homological) mirror symmetry.<\/p>\n<\/div><\/section>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Our research group studies algebraic varieties and noncommutative algebras, and their invariants, usually with an emphasis on Fano varieties or moduli spaces of sheaves and representations. 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