{"id":3676,"date":"2023-11-13T14:59:08","date_gmt":"2023-11-13T13:59:08","guid":{"rendered":"https:\/\/www.uni.lu\/research-en\/blog\/research-areas\/geometry-and-topology\/"},"modified":"2026-03-04T09:26:29","modified_gmt":"2026-03-04T08:26:29","slug":"geometry-and-topology","status":"publish","type":"research-areas","link":"https:\/\/www.uni.lu\/research-en\/research-areas\/geometry-and-topology\/","title":{"rendered":"Geometry and Topology"},"content":{"rendered":"\n<div class=\"wp-block-unilux-blocks-wrapper max-w-screen-3xl mx-auto section\">\n<section class=\"section no-padding-y wp-block-unilux-blocks-hero\">\n    <div class=\"hero hero--2 hero--overlay-top hero--overlay-bottom\">\n        \n<header class=\"wp-block-unilux-blocks-wrapper hero__header\">\n<div class=\"wp-block-unilux-blocks-wrapper hero__container\">\n<span class=\"hero__title__subject wp-block-unilux-blocks-plain-text\"><\/span>\n\n\n<h1 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"the-many-forms-of-modern-geometry-and-topology\"\n    >\nThe many forms of modern geometry and topology<\/h1>\n<\/div>\n<\/header>\n<figure class=\"wp-block-dev4-reusable-blocks-image hero__visual object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"ResearchArea DMATH GT ReachingForEneagons\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/ResearchArea_DMATH_GT_ReachingForEneagonsZkT4zl.jpg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/ResearchArea_DMATH_GT_ReachingForEneagonsZkT4zl-300x169.jpg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/ResearchArea_DMATH_GT_ReachingForEneagonsZkT4zl-1024x576.jpg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/ResearchArea_DMATH_GT_ReachingForEneagonsZkT4zl-768x432.jpg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/ResearchArea_DMATH_GT_ReachingForEneagonsZkT4zl-1536x864.jpg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/ResearchArea_DMATH_GT_ReachingForEneagonsZkT4zl.jpg 2000w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 16\/9; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure>\n<div class=\"wp-block-unilux-blocks-wrapper hero__body\">\n<div class=\"wp-block-unilux-blocks-wrapper hero__container\">\n<p class=\"wp-block-unilux-blocks-plain-text\">Exploring geometric objects, their topology and deformation: at the heart of mathematics and the language of science <\/p>\n\n\n<ul class=\"wp-block-unilux-blocks-custom-buttons btn-list\"><li class=\"wp-block-unilux-blocks-custom-button\"    aria-disabled=\"false\"\n    >\n    <a\n        role=\"link\"\n        aria-disabled=\"false\"\n                    href=\"#groups\"\n                target=\"_self\"\n        class=\"btn btn--primary\"\n            > Research groups<\/a>\n<\/li>\n\n\n<\/ul>\n<\/div>\n<\/div>\n    <\/div>\n<\/section><\/div>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h2 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"about\"\n    >\nAbout<\/h2>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Modern geometry and topology can take many forms, from understanding simple shapes to more abstract manifolds and higher structures.<br>Beyond their intrinsic beauty, these geometric and topological worlds often become model spaces for other sciences.<br>At DMATH, we study a plethora of geometric objects and how they deform, including moduli spaces, hyperbolic and Riemannian manifolds, and algebraic curves and varieties.<br><br>The following scientists and their groups contribute to the research in this area: Pieter Belmans, Karin Melnick, Sergei Merkulov, Hugo Parlier, Sarah Scherotzke, Jean-Marc Schlenker<br><\/p>\n<\/div>\n<\/div><\/section>\n\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h3 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"groups\"\n    >\nResearch groups<\/h3>\n\n\n<ul class=\"flex flex-wrap mt-24 -mx-16  wp-block-unilux-blocks-free-content-card\">\n    <li class=\"w-full sm:w-1\/2 lg:w-1\/3 px-16  wp-block-unilux-blocks-free-content-card-item\">\n    <div class=\"ulux-card card-residence bg-theme\">\n        <div class=\"ulux-card__container card__container\">\n                        <div class=\"ulux-card__visual wp-block-unilux-blocks-free-content-card-item-visual\">\n    \n<div class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Team-Scherotzke.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Team-Scherotzke-300x141.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Team-Scherotzke-1024x480.png 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Team-Scherotzke-768x360.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Team-Scherotzke-1536x719.png 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Team-Scherotzke.png 1580w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 4\/3; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div><\/div><div class=\"ulux-card__body wp-block-unilux-blocks-free-content-card-item-body\">\n    \n<div class=\"ulux-card__category wp-block-unilux-blocks-plain-text\">Mathematics<\/div>\n<h3 class=\"ulux-card__title has-text-align-left wp-block-unilux-blocks-heading\"        id=\"derived-algebraic-geometry-and-its-applications\"\n    >\n<strong>Derived Algebraic Geometry and its Applications<br><a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/derived-algebraic-geometry-and-its-applications\/\"><\/a><\/strong><\/h3>\n<div class=\"ulux-card__link-wrapper card__link wp-block-unilux-blocks-simple-cta\">\n    <a\n        href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/derived-algebraic-geometry-and-its-applications\/\"\n        class=\"link-text link-text--icon ulux-card__link link-text link-absolute\"\n        target=\"\"\n    >\n        <span class=\"link-text__body\">\n            <span class=\"link-text__name\">Learn more<\/span>\n        <\/span>\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>    <\/a>\n<\/div>\n<\/div>        <\/div>\n    <\/div>\n<\/li><li class=\"w-full sm:w-1\/2 lg:w-1\/3 px-16  wp-block-unilux-blocks-free-content-card-item\">\n    <div class=\"ulux-card card-residence bg-theme\">\n        <div class=\"ulux-card__container card__container\">\n                        <div class=\"ulux-card__visual wp-block-unilux-blocks-free-content-card-item-visual\">\n    \n<div class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1-300x300.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1-1024x1024.png 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1-150x150.png 150w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1-768x768.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1-1536x1536.png 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/loustau1.png 1637w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 4\/3; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div><\/div><div class=\"ulux-card__body wp-block-unilux-blocks-free-content-card-item-body\">\n    \n<div class=\"ulux-card__category wp-block-unilux-blocks-plain-text\">Mathematics <\/div>\n<h3 class=\"ulux-card__title has-text-align-left wp-block-unilux-blocks-heading\"        id=\"geometric-structure-and-moduli-spaces\"\n    >\nGeometric Structure and Moduli Spaces<br><a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/geometric-structure-and-moduli-spaces\/\"><\/a><\/h3>\n<div class=\"ulux-card__link-wrapper card__link wp-block-unilux-blocks-simple-cta\">\n    <a\n        href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/geometric-structure-and-moduli-spaces\/\"\n        class=\"link-text link-text--icon ulux-card__link link-text link-absolute\"\n        target=\"\"\n    >\n        <span class=\"link-text__body\">\n            <span class=\"link-text__name\">Learn more<\/span>\n        <\/span>\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>    <\/a>\n<\/div>\n<\/div>        <\/div>\n    <\/div>\n<\/li><li class=\"w-full sm:w-1\/2 lg:w-1\/3 px-16  wp-block-unilux-blocks-free-content-card-item\">\n    <div class=\"ulux-card card-residence bg-theme\">\n        <div class=\"ulux-card__container card__container\">\n                        <div class=\"ulux-card__visual wp-block-unilux-blocks-free-content-card-item-visual\">\n    \n<div class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Diffeomorphism.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Diffeomorphism-300x300.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Diffeomorphism-150x150.png 150w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Diffeomorphism.png 739w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 4\/3; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div><\/div><div class=\"ulux-card__body wp-block-unilux-blocks-free-content-card-item-body\">\n    \n<div class=\"ulux-card__category wp-block-unilux-blocks-plain-text\">Mathematics<\/div>\n<h3 class=\"ulux-card__title has-text-align-left wp-block-unilux-blocks-heading\"        id=\"group-actions-geometric-structures-and-smooth-dynamics\"\n    >\n<strong>Group Actions, Geometric Structures, and Smooth Dynamics<\/strong><\/h3>\n<div class=\"ulux-card__link-wrapper card__link wp-block-unilux-blocks-simple-cta\">\n    <a\n        href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/group-actions-geometric-structures-and-smooth-dynamics\/\"\n        class=\"link-text link-text--icon ulux-card__link link-text link-absolute\"\n        target=\"\"\n    >\n        <span class=\"link-text__body\">\n            <span class=\"link-text__name\">Learn more<\/span>\n        <\/span>\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>    <\/a>\n<\/div>\n<\/div>        <\/div>\n    <\/div>\n<\/li><\/ul><\/div><\/section>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h3 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"research-takes-place-at\"\n    >\nResearch takes place at:<\/h3>\n\n\n<ul class=\"wp-block-unilux-blocks-button-list\">\n    <li class=\"normal wp-block-unilux-blocks-button-list-item\">\n    <a\n            href=\"https:\/\/www.uni.lu\/fstm-en\/\"\n            class=\"quick-link wp-block-unilux-blocks-anchor\"        target=\"\"\n>\n    \n<span class=\"wp-block-unilux-blocks-wrapper quick-link__container\"><figure class=\"wp-block-dev4-reusable-blocks-image quick-link__img object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2026\/03\/01200346\/university-of-luxembourg-fstm-symbol-only.svg\"\n                    style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 1\/1; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure>\n\n\n<span class=\"quick-link__name wp-block-unilux-blocks-plain-text\">Faculty of Science, Technology and Medicine (FSTM)<\/span>\n\n<svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg><\/span>\n<\/a>\n<\/li><li class=\"image-rounded wp-block-unilux-blocks-button-list-item\">\n    <a\n            href=\"https:\/\/www.uni.lu\/fstm-en\/research-departments\/department-of-mathematics\/\"\n            class=\"quick-link wp-block-unilux-blocks-anchor\"        target=\"\"\n>\n    \n<span class=\"wp-block-unilux-blocks-wrapper quick-link__container\"><figure class=\"wp-block-dev4-reusable-blocks-image quick-link__img object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"Logo of Department of Mathematics\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1-300x300.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1-1024x1024.png 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1-150x150.png 150w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1-768x768.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1-1536x1536.png 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Mathematics-2048x2048-1.png 2048w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 1\/1; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure>\n\n\n<span class=\"quick-link__name wp-block-unilux-blocks-plain-text\">Department of Mathematics<\/span>\n\n<svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg><\/span>\n<\/a>\n<\/li><\/ul>\n<\/div><\/section>\n\n\n<section class=\"section section wp-block-unilux-blocks-quick-link-discover-section\">\n    <div class=\"container xl:max-w-screen-xl\">\n        \n<h2 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"discover-more\"\n    >\nDiscover more<\/h2>\n\n<ul class=\"wp-block-unilux-blocks-quick-link-discover quick-link-list\">\n<li class=\"wp-block-unilux-blocks-quick-link-discover-item\">\n    <a\n                    href=\"https:\/\/www.uni.lu\/en\/about\/profile\/mission-strategy-values\/#strategic-development-areas\"\n                    class=\"quick-link\"\n            target=\"\"\n    >\n            <span class=\"quick-link__container\">\n                <span class=\"quick-link__text\">\n                    Key areas                <\/span>\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>            <\/span>\n    <\/a>\n<\/li>\n\n\n\n<li class=\"wp-block-unilux-blocks-quick-link-discover-item\">\n    <a\n                    href=\"https:\/\/www.uni.lu\/en\/about\/organisation\/faculties-departments\/\"\n                    class=\"quick-link\"\n            target=\"\"\n    >\n            <span class=\"quick-link__container\">\n                <span class=\"quick-link__text\">\n                    Faculties                <\/span>\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>            <\/span>\n    <\/a>\n<\/li>\n\n\n\n<li class=\"wp-block-unilux-blocks-quick-link-discover-item\">\n    <a\n                    href=\"https:\/\/www.uni.lu\/en\/about\/organisation\/centres\/\"\n                    class=\"quick-link\"\n            target=\"\"\n    >\n            <span class=\"quick-link__container\">\n                <span class=\"quick-link__text\">\n                    Interdisciplinary centres                <\/span>\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>            <\/span>\n    <\/a>\n<\/li>\n<\/ul>\n    <\/div>\n<\/section>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3675,"parent":0,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Geometry and Topology","uluxPrePostTitle":"Research area","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false},"field-of-interest":[54],"organisation":[95,59],"authorship":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Geometry and Topology - Research area I 8xav福利导航 of Luxembourg<\/title>\n<meta name=\"description\" content=\"Modern geometry and topology can take many forms, from understanding simple shapes to more abstract manifolds and higher structures.Beyond their intrinsic\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.uni.lu\/research-en\/research-areas\/geometry-and-topology\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Geometry and Topology\" \/>\n<meta property=\"og:description\" content=\"Modern geometry and topology can take many forms, from understanding simple shapes to more abstract manifolds and higher structures.Beyond their intrinsic\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.uni.lu\/research-en\/research-areas\/geometry-and-topology\/\" \/>\n<meta property=\"og:site_name\" content=\"Research EN\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-04T08:26:29+00:00\" \/>\n<meta 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