{"id":3672,"date":"2023-11-13T14:58:54","date_gmt":"2023-11-13T13:58:54","guid":{"rendered":"https:\/\/www.uni.lu\/research-en\/blog\/research-areas\/algebra-and-number-theory\/"},"modified":"2026-03-04T09:27:10","modified_gmt":"2026-03-04T08:27:10","slug":"algebra-and-number-theory","status":"publish","type":"research-areas","link":"https:\/\/www.uni.lu\/research-en\/research-areas\/algebra-and-number-theory\/","title":{"rendered":"Algebra and Number Theory"},"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=\"structure-in-algebra-number-theory-and-geometry\"\n    >\nStructure in algebra, number theory and geometry<\/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=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/27165619\/Algebra-and-Number-Theory.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/27165619\/Algebra-and-Number-Theory-300x300.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/27165619\/Algebra-and-Number-Theory-1019x1024.png 1019w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/27165619\/Algebra-and-Number-Theory-150x150.png 150w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/27165619\/Algebra-and-Number-Theory-768x771.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/27165619\/Algebra-and-Number-Theory.png 1330w\"\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\">Using algebraic structures: from fundamental research to real-life application<\/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>At its foundation algebra is concerned with polynomial equations and their solutions. In the Algebra &amp; Number Theory (ANT) research area, we use these to model and study objects with a very rich and deep structure, like varieties and groups in algebraic and arithmetic geometry, modular forms in number theory, or operads.<br>We then study invariants, symmetries, and deformations of these algebraic structures to understand how they behave under various transformations and how they are related to one another. We regularly combine these more abstract questions with computational tools and real-life applications in cryptography. Our research often involves aspects of representation theory and topology.<br>The following scientists and their groups contribute to the research in this area: Pieter Belmans, Sergei Merkulov, Antonella Perucca, Sarah Scherotzke, Bruno Teheux, Gabor Wiese.<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=\"Antonella Perucca Black board\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/perucca-board.jpg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/perucca-board-300x145.jpg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/perucca-board-1024x495.jpg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/perucca-board-768x372.jpg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/perucca-board-1536x743.jpg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/perucca-board.jpg 1939w\"\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\"><\/div>\n<h3 class=\"ulux-card__title has-text-align-left wp-block-unilux-blocks-heading\"        id=\"number-theory-and-arithmetic-geometry\"\n    >\nNumber Theory and Arithmetic Geometry<strong><br><a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/antonella-peruccas-research-group\/\"><\/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\/number-theory-and-arithmetic-geometry\/\"\n        title=\"Learn more\"\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=\"Sarah Scherotzke\u2019s research group\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Picture_1.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Picture_1-300x141.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Picture_1-1024x480.png 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Picture_1-768x360.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Picture_1-1536x719.png 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Picture_1.png 1580w\"\n                style=\"object-position: 86.00% 57.00%; font-family: &quot;object-fit: cover; object-position: 86.00% 57.00%;&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\"><\/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><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><\/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        title=\"Learn more\"\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=\"Team Teheux\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Teheux_Overview.jpg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Teheux_Overview-300x205.jpg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Teheux_Overview-1024x700.jpg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Teheux_Overview-768x525.jpg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Teheux_Overview-1536x1051.jpg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/8\/2023\/11\/Teheux_Overview.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: 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\"><\/div>\n<h3 class=\"ulux-card__title has-text-align-left wp-block-unilux-blocks-heading\"        id=\"non-classical-logics\"\n    >\n<strong>Non-Classical Logics<br><a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/non-classical-logics\/team-teheux\/\"><\/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\/non-classical-logics\/\"\n        title=\"Learn more\"\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":3671,"parent":0,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Algebra and Number Theory","uluxPrePostTitle":"","_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>Algebra and Number Theory - Research area I University of Luxembourg<\/title>\n<meta name=\"description\" content=\"At its foundation algebra is concerned with polynomial equations and their solutions. In the Algebra &amp; Number Theory (ANT) research area, we use these\" \/>\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\/algebra-and-number-theory\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Algebra and Number Theory\" \/>\n<meta property=\"og:description\" content=\"At its foundation algebra is concerned with polynomial equations and their solutions. 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