FGTR 2025 \u2014 Finite Groups and Their Representations<\/title>\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,600;1,400;1,500&family=DM+Mono:wght@300;400;500&family=Outfit:wght@300;400;500;600&display=swap\" rel=\"stylesheet\">\n<script>\nMathJax = { tex: { inlineMath: [['\\\\(','\\\\)']] } };\n<\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-chtml.js\" async><\/script>\n\n<style>\n:root {\n --cream: #F5F0E8;\n --ink: #1A1610;\n --rust: #B84A2F;\n --gold: #C99A2E;\n --slate: #3D4A5C;\n --mist: #E8EDF4;\n --rule: #C8BFA8;\n --garamond: 'EB Garamond', Georgia, serif;\n --mono: 'DM Mono', monospace;\n --sans: 'Outfit', sans-serif;\n}\n*, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }\nbody { background: #eee; padding: 2rem; font-family: var(--garamond); color: var(--ink); }\n\n.conf-block {\n max-width: 980px; margin: 0 auto; background: var(--cream);\n border: 1px solid var(--rule);\n box-shadow: 4px 4px 0 var(--rule), 8px 8px 0 #d8cdb8;\n overflow: hidden;\n}\n\n.conf-hero {\n background: var(--slate); color: var(--cream);\n padding: 3.5rem 3rem 2.5rem; position: relative; overflow: hidden;\n}\n.conf-hero::before {\n content: 'G S p B F R';\n position: absolute; top: -10px; right: -20px;\n font-family: var(--garamond); font-size: 9rem;\n letter-spacing: 0.05em; color: rgba(255,255,255,0.04);\n pointer-events: none; line-height: 1;\n}\n.conf-hero-tag {\n font-family: var(--mono); font-size: 0.7rem; letter-spacing: 0.18em;\n text-transform: uppercase; color: var(--gold); margin-bottom: 1rem;\n display: flex; align-items: center; gap: 0.5rem;\n}\n.conf-hero-tag::before { content: ''; display: inline-block; width: 24px; height: 1px; background: var(--gold); }\n.conf-title {\n font-family: var(--garamond); font-size: clamp(1.9rem, 4vw, 3rem);\n font-weight: 500; line-height: 1.15; margin-bottom: 0.7rem; letter-spacing: -0.01em;\n}\n.conf-subtitle {\n font-family: var(--garamond); font-style: italic; font-size: 1.1rem;\n color: rgba(245,240,232,0.7); margin-bottom: 1.8rem;\n}\n.conf-meta { display: flex; flex-wrap: wrap; gap: 1.5rem; font-family: var(--sans); font-size: 0.8rem; color: rgba(245,240,232,0.75); }\n.conf-meta span { display: flex; align-items: center; gap: 0.4rem; }\n.conf-meta svg { width: 13px; height: 13px; opacity: 0.7; }\n\n.conf-nav { display: flex; border-bottom: 1px solid var(--rule); background: #EDE8DE; overflow-x: auto; scrollbar-width: none; }\n.conf-nav::-webkit-scrollbar { display: none; }\n.conf-tab {\n padding: 0.9rem 1.4rem; font-family: var(--sans); font-size: 0.78rem;\n font-weight: 500; letter-spacing: 0.06em; text-transform: uppercase;\n cursor: pointer; border: none; background: none; color: #7A6E60;\n white-space: nowrap; border-bottom: 2px solid transparent; margin-bottom: -1px;\n transition: color 0.2s, border-color 0.2s;\n}\n.conf-tab:hover { color: var(--ink); }\n.conf-tab.active { color: var(--rust); border-bottom-color: var(--rust); }\n\n.conf-panels { padding: 2.5rem 3rem; }\n.conf-panel { display: none; }\n.conf-panel.active { display: block; }\n\n.section-heading {\n font-family: var(--garamond); font-size: 1.45rem; font-weight: 500;\n margin-bottom: 0.3rem; display: flex; align-items: center; gap: 0.7rem;\n}\n.section-heading::after { content: ''; flex: 1; height: 1px; background: var(--rule); }\n.section-sub { font-family: var(--garamond); font-style: italic; font-size: 0.92rem; color: #7A6E60; margin-bottom: 2rem; }\n\n.overview-grid { display: grid; grid-template-columns: 1fr 260px; gap: 2.5rem; }\n.overview-body { font-size: 1.05rem; line-height: 1.8; color: #2E2820; }\n.overview-body p + p { margin-top: 1em; }\n.info-card { background: var(--mist); border: 1px solid var(--rule); padding: 1.4rem 1.5rem; margin-bottom: 1rem; }\n.info-card-label { font-family: var(--mono); font-size: 0.65rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--rust); margin-bottom: 0.4rem; }\n.info-card-value { font-family: var(--sans); font-size: 0.88rem; color: var(--ink); line-height: 1.5; }\n\n.speakers-grid { display: grid; grid-template-columns: repeat(auto-fill, minmax(260px, 1fr)); gap: 1.5rem; }\n.speaker-card { border: 1px solid var(--rule); cursor: pointer; transition: box-shadow 0.2s, transform 0.2s; background: #fff; }\n.speaker-card:hover { box-shadow: 3px 3px 0 var(--rust); transform: translate(-1px,-1px); }\n.speaker-info { padding: 1.4rem 1.4rem 1.5rem; }\n.speaker-name { font-family: var(--garamond); font-size: 1.1rem; font-weight: 500; margin-bottom: 0.15rem; }\n.speaker-affil { font-family: var(--sans); font-size: 0.75rem; color: #7A6E60; margin-bottom: 0.6rem; }\n.speaker-topic { font-family: var(--garamond); font-style: italic; font-size: 0.88rem; color: var(--rust); line-height: 1.4; }\n.speaker-tag { display: inline-block; font-family: var(--mono); font-size: 0.6rem; letter-spacing: 0.1em; background: var(--mist); color: var(--slate); padding: 0.15rem 0.5rem; margin-top: 0.6rem; text-transform: uppercase; }\n\n.abstract-item { border-left: 3px solid var(--rule); padding: 0 0 0 1.5rem; margin-bottom: 2.2rem; transition: border-color 0.2s; }\n.abstract-item:hover { border-left-color: var(--rust); }\n.abstract-item:last-child { margin-bottom: 0; }\n.abstract-speaker { font-family: var(--sans); font-size: 0.72rem; font-weight: 500; letter-spacing: 0.1em; text-transform: uppercase; color: var(--slate); margin-bottom: 0.3rem; }\n.abstract-title { font-family: var(--garamond); font-size: 1.2rem; font-weight: 500; margin-bottom: 0.2rem; cursor: pointer; display: flex; align-items: baseline; justify-content: space-between; gap: 1rem; }\n.abstract-title .toggle-arrow { font-size: 0.75rem; color: var(--rust); flex-shrink: 0; transition: transform 0.25s; }\n.abstract-meta { font-family: var(--mono); font-size: 0.67rem; color: #9A8E80; letter-spacing: 0.05em; margin-bottom: 0.6rem; }\n.abstract-body { font-size: 0.97rem; line-height: 1.75; color: #2E2820; max-height: 0; overflow: hidden; transition: max-height 0.4s ease; }\n.abstract-body.open { max-height: 800px; }\n.abstract-body p { margin-top: 0.5em; }\n.abstract-keywords { margin-top: 0.8em; font-family: var(--mono); font-size: 0.68rem; color: var(--slate); letter-spacing: 0.04em; }\n.abstract-keywords span { display: inline-block; background: var(--mist); padding: 0.1rem 0.5rem; margin: 0.1rem 0.2rem 0 0; }\n\n.schedule-day-label { font-family: var(--mono); font-size: 0.68rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--rust); margin: 2rem 0 0.8rem; display: flex; align-items: center; gap: 0.7rem; }\n.schedule-day-label::after { content: ''; flex: 1; height: 1px; background: var(--rule); }\n.schedule-day-label:first-child { margin-top: 0; }\n.schedule-row { display: grid; grid-template-columns: 90px 1fr; gap: 0 1.5rem; padding: 0.7rem 0; border-bottom: 1px solid #e8e0d0; align-items: start; }\n.schedule-row:last-child { border-bottom: none; }\n.sch-time { font-family: var(--mono); font-size: 0.75rem; color: #7A6E60; padding-top: 0.1rem; letter-spacing: 0.03em; }\n.sch-event { font-size: 0.97rem; line-height: 1.5; }\n.sch-type { display: inline-block; font-family: var(--mono); font-size: 0.6rem; letter-spacing: 0.1em; padding: 0.1rem 0.45rem; text-transform: uppercase; margin-left: 0.5rem; vertical-align: middle; }\n.sch-type.talk { background: #EDF2FA; color: var(--slate); }\n.sch-type.social { background: #FBF0E6; color: #9A5020; }\n.sch-type.break { background: #F0F0F0; color: #888; }\n\n.gallery-intro { font-family: var(--garamond); font-style: italic; font-size: 0.95rem; color: #7A6E60; margin-bottom: 1.5rem; line-height: 1.6; }\n.gallery-grid { display: grid; grid-template-columns: repeat(3, 1fr); gap: 6px; }\n.gallery-cell { aspect-ratio: 4\/3; background: var(--mist); display: flex; align-items: center; justify-content: center; overflow: hidden; cursor: zoom-in; }\n.gallery-cell:first-child { grid-column: span 2; aspect-ratio: 16\/9; }\n.gallery-cell-inner { width: 100%; height: 100%; display: flex; flex-direction: column; align-items: center; justify-content: center; gap: 0.5rem; background: linear-gradient(135deg, #dce4f0 0%, #c8d4e6 50%, #b8c8e0 100%); transition: transform 0.3s; }\n.gallery-cell:hover .gallery-cell-inner { transform: scale(1.03); }\n.gallery-cell-inner .icon { font-size: 2.2rem; opacity: 0.35; }\n.gallery-cell-inner .caption { font-family: var(--sans); font-size: 0.65rem; letter-spacing: 0.06em; text-transform: uppercase; color: var(--slate); opacity: 0.7; }\n.gallery-upload-note { margin-top: 1rem; font-family: var(--mono); font-size: 0.7rem; color: #9A8E80; letter-spacing: 0.04em; text-align: center; padding: 0.8rem; border: 1px dashed var(--rule); }\n\n.info-two-col { display: grid; grid-template-columns: 1fr 1fr; gap: 2rem; }\n.info-block { margin-bottom: 2rem; }\n.info-block h4 { font-family: var(--garamond); font-size: 1.05rem; font-weight: 500; margin-bottom: 0.5rem; border-bottom: 1px solid var(--rule); padding-bottom: 0.3rem; }\n.info-block p, .info-block li { font-family: var(--garamond); font-size: 0.95rem; line-height: 1.7; color: #2E2820; }\n.info-block ul { list-style: none; padding: 0; }\n.info-block ul li::before { content: '\u2192 '; color: var(--rust); font-family: var(--mono); }\n.org-list { display: flex; flex-direction: column; gap: 0.6rem; margin-top: 0.5rem; }\n.org-person { display: flex; flex-direction: column; }\n.org-person strong { font-family: var(--sans); font-size: 0.82rem; font-weight: 500; }\n.org-person span { font-family: var(--garamond); font-style: italic; font-size: 0.82rem; color: #7A6E60; }\n\n.conf-footer { background: var(--ink); color: rgba(245,240,232,0.5); font-family: var(--mono); font-size: 0.65rem; letter-spacing: 0.06em; padding: 1rem 3rem; display: flex; align-items: center; justify-content: space-between; }\n.conf-footer a { color: var(--gold); text-decoration: none; }\n\n.modal-overlay { display: none; position: fixed; inset: 0; background: rgba(26,22,16,0.7); z-index: 1000; align-items: center; justify-content: center; padding: 2rem; }\n.modal-overlay.open { display: flex; }\n.modal-box { background: var(--cream); max-width: 560px; width: 100%; max-height: 80vh; overflow-y: auto; border: 1px solid var(--rule); box-shadow: 8px 8px 0 rgba(26,22,16,0.25); }\n.modal-header { display: flex; align-items: center; gap: 1rem; padding: 1.5rem; border-bottom: 1px solid var(--rule); background: var(--slate); color: var(--cream); }\n.modal-avatar { width: 64px; height: 64px; border-radius: 50%; background: linear-gradient(135deg, #d8e0ec, #b8c8e0); display: flex; align-items: center; justify-content: center; font-size: 1.4rem; flex-shrink: 0; font-family: var(--garamond); color: var(--slate); font-weight: 500; }\n.modal-name { font-family: var(--garamond); font-size: 1.3rem; font-weight: 500; }\n.modal-affil { font-family: var(--sans); font-size: 0.75rem; color: rgba(245,240,232,0.65); }\n.modal-body { padding: 1.5rem; }\n.modal-body p { font-size: 0.97rem; line-height: 1.75; color: #2E2820; }\n.modal-close { background: none; border: none; cursor: pointer; color: var(--cream); font-size: 1.4rem; margin-left: auto; line-height: 1; padding: 0.2rem; opacity: 0.6; transition: opacity 0.2s; }\n.modal-close:hover { opacity: 1; }\n\n@media (max-width: 680px) {\n .overview-grid { grid-template-columns: 1fr; }\n .conf-panels { padding: 2rem 1.5rem; }\n .info-two-col { grid-template-columns: 1fr; }\n .gallery-grid { grid-template-columns: repeat(2,1fr); }\n}\n::-webkit-scrollbar { width: 5px; height: 5px; }\n::-webkit-scrollbar-track { background: transparent; }\n::-webkit-scrollbar-thumb { background: var(--rule); border-radius: 3px; }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"conf-block\" id=\"conf-block-fgtr2025\">\n\n <div class=\"conf-hero\">\n <div class=\"conf-hero-tag\">Workshop \u00b7 Algebra \u00b7 Group Theory<\/div>\n <h1 class=\"conf-title\">Finite Groups and<br>Their Representations<\/h1>\n <p class=\"conf-subtitle\">FGTR 2025 \u00b7 Mathematics Research Center, ASOIU<\/p>\n <div class=\"conf-meta\">\n <span>\n <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 1a5 5 0 100 10A5 5 0 008 1zM0 8a8 8 0 1116 0A8 8 0 010 8z\"\/><path d=\"M7.5 4.5v4l2.5 1.5.5-.87L8.5 8V4.5z\"\/><\/svg>\n June 18\u201320, 2025\n <\/span>\n <span>\n <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 0C5.24 0 3 2.24 3 5c0 3.75 5 11 5 11s5-7.25 5-11c0-2.76-2.24-5-5-5zm0 7.5a2.5 2.5 0 110-5 2.5 2.5 0 010 5z\"\/><\/svg>\n Baku, Azerbaijan\n <\/span>\n <span>\n <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M7 0H2a1 1 0 00-1 1v2h14V1a1 1 0 00-1-1H7zm7 4H1v10a1 1 0 001 1h12a1 1 0 001-1V4z\"\/><\/svg>\n FGTR 2025\n <\/span>\n <\/div>\n <\/div>\n\n <nav class=\"conf-nav\" role=\"tablist\">\n <button class=\"conf-tab active\" data-panel=\"overview\" role=\"tab\">Overview<\/button>\n <button class=\"conf-tab\" data-panel=\"speakers\" role=\"tab\">Invited Speakers<\/button>\n <button class=\"conf-tab\" data-panel=\"abstracts\" role=\"tab\">Abstracts<\/button>\n <button class=\"conf-tab\" data-panel=\"schedule\" role=\"tab\">Schedule<\/button>\n <button class=\"conf-tab\" data-panel=\"gallery\" role=\"tab\">Gallery<\/button>\n <button class=\"conf-tab\" data-panel=\"info\" role=\"tab\">Further Info<\/button>\n <\/nav>\n\n <div class=\"conf-panels\">\n\n <section class=\"conf-panel active\" id=\"panel-overview\">\n <div class=\"section-heading\">About the Workshop<\/div>\n <p class=\"section-sub\">June 18\u201320, 2025 \u00b7 Baku, Azerbaijan<\/p>\n <div class=\"overview-grid\">\n <div class=\"overview-body\">\n <p>This three-day workshop brings together researchers working in the theory of finite groups and their representations, with a particular focus on fusion systems, block theory, biset functors, and character-theoretic methods.<\/p>\n <p>The programme features seven invited talks by leading specialists from Turkey, the United States, and Azerbaijan, covering topics ranging from the Alperin\u2013McKay conjecture and Feit’s conjecture to categorical decompositions of biset functors and weight conjectures for exotic fusion systems.<\/p>\n <p>The workshop is organized by the <em>Mathematics Research Center of ASOIU<\/em> (Azerbaijan State Oil and Industry University), Baku.<\/p>\n <\/div>\n <div class=\"overview-sidebar\">\n <div class=\"info-card\"><div class=\"info-card-label\">Dates<\/div><div class=\"info-card-value\">June 18\u201320, 2025<\/div><\/div>\n <div class=\"info-card\"><div class=\"info-card-label\">Venue<\/div><div class=\"info-card-value\">Mathematics Research Center<br>ASOIU, Baku, Azerbaijan<\/div><\/div>\n <div class=\"info-card\"><div class=\"info-card-label\">Format<\/div><div class=\"info-card-value\">In-person<\/div><\/div>\n <\/div>\n <\/div>\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-speakers\">\n <div class=\"section-heading\">Invited Speakers<\/div>\n <p class=\"section-sub\">Click a card to view biography<\/p>\n <div class=\"speakers-grid\">\n <div class=\"speaker-card\" data-speaker=\"0\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Laurence Barker<\/div>\n <div class=\"speaker-affil\">Bilkent University<\/div>\n <div class=\"speaker-topic\">The pointed fusion system of a block<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"1\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Robert Boltje<\/div>\n <div class=\"speaker-affil\">University of California, Santa Cruz<\/div>\n <div class=\"speaker-topic\">On a conjecture of Feit<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"2\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">M. Yasir K\u0131zmaz<\/div>\n <div class=\"speaker-affil\">Bilkent University<\/div>\n <div class=\"speaker-topic\">A generalization of the Alperin Fusion theorem and its applications<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"3\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Nariel Monteiro<\/div>\n <div class=\"speaker-affil\">University of California, Santa Cruz<\/div>\n <div class=\"speaker-topic\">Links between character triples<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"4\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Ruslan M\u00fcsl\u00fcmov<\/div>\n <div class=\"speaker-affil\">ADA University<\/div>\n <div class=\"speaker-topic\">A Categorical Decomposition of ℂ×-fibered <i>p<\/i>-biset Functors<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"5\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">\u0130pek Tuvay<\/div>\n <div class=\"speaker-affil\">Mimar Sinan Fine Arts University<\/div>\n <div class=\"speaker-topic\">Weight conjectures for Parker\u2013Semeraro fusion systems<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"6\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Deniz Y\u0131lmaz<\/div>\n <div class=\"speaker-affil\">Bilkent University<\/div>\n <div class=\"speaker-topic\">Diagonal <i>p<\/i>-permutation functors \u00b7 Functorial equivalences between blocks<\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-abstracts\">\n <div class=\"section-heading\">Abstracts<\/div>\n <p class=\"section-sub\">Click a title to expand the abstract<\/p>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Laurence Barker \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>The pointed fusion system of a block<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Thursday, June 19 \u00b7 09:30<\/div>\n <div class=\"abstract-body\">\n <p>The pointed fusion system of a block is a category and a poset that refines the fusion system. Like the fusion system, it is a local invariant in that it is determined by the source algebra. Unlike the fusion system, it determines the number of simple modules. We shall show that it satisfies a generalization of the saturation condition. If it could be argued that mysterious invariants might be needed to cut inroads to the outstanding conjectures of block theory, then the pointed fusion system fits the bill: we do not know whether it coincides with what Th\u00e9venaz called the Puig category.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>fusion systems<\/span><span>block theory<\/span><span>source algebra<\/span><span>Puig category<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Robert Boltje \u00b7 University of California, Santa Cruz<\/div>\n <div class=\"abstract-title\" data-abstract>On a conjecture of Feit<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Wednesday, June 18 \u00b7 09:30<\/div>\n <div class=\"abstract-body\">\n <p>In 1979, Walter Feit suggested to use the classification of finite simple groups to decide if the following statement holds: If \\(\\chi\\) is an irreducible character of a finite group \\(G\\) and if \\(n\\) is the smallest positive integer such that all values of \\(\\chi\\) belong to the \\(n\\)-th cyclotomic field then \\(G\\) has an element of order \\(n\\). In 1986, Ferguson\u2013Turull and Amit\u2013Chillag proved independently that this holds if \\(G\\) is solvable. Not much progress has been made in the following years. Only recently, in joint work with A. Kleshchev, G. Navarro, and Ph. H. Tiep, we showed that the answer is yes, provided that every non-abelian finite simple group satisfies a condition that we call the inductive Feit condition. This talk describes the reduction theorem and other related results and conjectures.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>Feit conjecture<\/span><span>irreducible characters<\/span><span>cyclotomic fields<\/span><span>finite simple groups<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">M. Yasir K\u0131zmaz \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>A generalization of the Alperin Fusion theorem and its applications<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Wednesday, June 18 \u00b7 11:30<\/div>\n <div class=\"abstract-body\">\n <p>In this talk, we aim to present a generalization of the Alperin\u2013Goldschmidt fusion theorem for saturated fusion systems. Our approach introduces the notion of \\(\\mathcal{F}\\)-essential subgroups relative to a strongly \\(\\mathcal{F}\\)-closed subgroup \\(P\\) of a \\(p\\)-group \\(S\\). We show that any \\(\\mathcal{F}\\)-isomorphism between subgroups of \\(P\\) can be decomposed using some automorphisms of \\(P\\) and these relative \\(\\mathcal{F}\\)-essential subgroups. When \\(P\\) is taken to be equal to \\(S\\), the Alperin\u2013Goldschmidt fusion theorem can be obtained as a special case.<\/p>\n <p>A \\(p\\)-group \\(P\\) is strongly resistant in saturated fusion systems if \\(P \\unlhd \\mathcal{F}\\) whenever there is an over \\(p\\)-group \\(S\\) and a saturated fusion system \\(\\mathcal{F}\\) on \\(S\\) such that \\(P\\) is strongly \\(\\mathcal{F}\\)-closed. We show that several classes of \\(p\\)-groups are strongly resistant. We also give a new necessary and sufficient criterion for a strongly \\(\\mathcal{F}\\)-closed subgroup to be normal in \\(\\mathcal{F}\\). These results are obtained as a consequence of developing a theory of quasi and semi-saturated fusion systems, which seems to be interesting in its own right.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>Alperin\u2013Goldschmidt theorem<\/span><span>saturated fusion systems<\/span><span>essential subgroups<\/span><span>strongly closed<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Nariel Monteiro \u00b7 University of California, Santa Cruz<\/div>\n <div class=\"abstract-title\" data-abstract>Links between character triples<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Thursday, June 19 \u00b7 14:30<\/div>\n <div class=\"abstract-body\">\n <p>We will introduce the notion of a link between character triples. The motivation to consider this notion has multiple reasons. Firstly, links between character triples induce special character triple isomorphisms. This provides a new perspective for isomorphisms between character triples and a different conceptual understanding. Secondly, links between character triples provide equivalent reformulations of complicated conditions (involving projective representations) that play a fundamental role in the reductions of the McKay conjecture and the Feit conjecture to finite simple groups. This is joint work with Robert Boltje and John Revere McHugh.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>character triples<\/span><span>McKay conjecture<\/span><span>projective representations<\/span><span>finite simple groups<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Ruslan M\u00fcsl\u00fcmov \u00b7 ADA University<\/div>\n <div class=\"abstract-title\" data-abstract>A Categorical Decomposition of ℂ×-fibered p-biset Functors<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Wednesday, June 18 \u00b7 14:30<\/div>\n <div class=\"abstract-body\">\n <p>We generalize Bouc’s construction of orthogonal idempotents in the double Burnside algebra to the setting of the double \\(\\mathbb{C}^\\times\\)-fibered Burnside algebra. This yields a structural decomposition of the evaluations of \\(\\mathbb{C}^\\times\\)-fibered biset functors on finite groups. We then construct a complete set of orthogonal idempotents in the category of \\(\\mathbb{C}^\\times\\)-fibered \\(p\\)-biset functors, leading to a categorical decomposition of this category into subcategories indexed by isomorphism classes of atoric \\(p\\)-groups. Furthermore, we introduce the notion of <em>vertices<\/em> for indecomposable functors and establish that the \\(\\mathrm{Ext}\\)-groups between simple functors with distinct vertices vanish. As an application, we describe a set containing composition factors of the monomial Burnside functor, thereby providing new insights into its structure. Additionally, we develop a technique for analyzing fibered biset functors via their underlying biset structures. This is a joint work with Olcay Co\u015fkun.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>biset functors<\/span><span>Burnside algebra<\/span><span>orthogonal idempotents<\/span><span>p-groups<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">\u0130pek Tuvay \u00b7 Mimar Sinan Fine Arts University<\/div>\n <div class=\"abstract-title\" data-abstract>Weight conjectures for Parker\u2013Semeraro fusion systems<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Friday, June 20 \u00b7 09:30<\/div>\n <div class=\"abstract-body\">\n <p>Weight conjectures for fusion systems are conjectural statements for fusion systems which are motivated by local-global conjectures in block theory and were put forward by Kessar, Linckelmann, Lynd and Semeraro in 2019. In fact, the interest in weight conjectures goes beyond the local-global conjectures from block theory. They apply equally well in the situation where the fusion system is block-exotic. In the first part of the talk, I will introduce these conjectures and mention their link to conjectures in block theory. Then I will present the results which verify these conjectures for the family of Parker\u2013Semeraro fusion systems which contains 27 block-exotic fusion systems. This is a joint work with Kessar, Semeraro and Serwene.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>weight conjectures<\/span><span>Parker\u2013Semeraro systems<\/span><span>block-exotic fusion systems<\/span><span>block theory<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Deniz Y\u0131lmaz \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>Diagonal p-permutation functors<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Thursday, June 19 \u00b7 10:30<\/div>\n <div class=\"abstract-body\">\n <p>Let \\(p\\) be a prime number and let \\(\\mathbb{F}\\) be an algebraically closed field of characteristic \\(0\\) or \\(p\\). In this talk we introduce the notion of diagonal \\(p\\)-permutation functors over \\(\\mathbb{F}\\). We show that the simple diagonal \\(p\\)-permutation functors \\(S_{L,u,V}\\) are parametrized by triples \\((L,u,V)\\) where \\(L\\) is a \\(p\\)-group, \\(u\\) is a \\(p’\\)-automorphism of \\(L\\) and \\(V\\) is a simple \\(\\mathbb{F}\\mathrm{Out}(L,u)\\)-module. We also describe the evaluations of the simple functors. In particular, if \\(\\mathbb{F}\\) has characteristic \\(p\\), we show that for a finite group \\(G\\), the dimension of \\(S_{L,1,\\mathbb{F}}(G)\\) is equal to the number of conjugacy classes of \\(p\\)-regular elements of \\(G\\) with defect isomorphic to \\(L\\). We finally prove that if \\(\\mathbb{F}\\) is of characteristic zero, then the category of diagonal \\(p\\)-permutation functors is semisimple. This is a joint work with Bouc.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>p-permutation functors<\/span><span>simple functors<\/span><span>p-groups<\/span><span>semisimple category<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Deniz Y\u0131lmaz \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>Functorial equivalences between blocks of finite groups<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Friday, June 20 \u00b7 10:30<\/div>\n <div class=\"abstract-body\">\n <p>We will talk about the notion of functorial equivalences between blocks of finite groups, a notion introduced using the theory of diagonal \\(p\\)-permutation functors. We investigate the invariants preserved by functorial equivalences and their relations with other well-studied equivalences. We prove a finiteness theorem in the spirit of Donovan’s and Puig’s finiteness conjectures: there are only finitely many blocks of finite groups with a given defect group, up to functorial equivalence. We also give a reformulation of Alperin’s weight conjecture in terms of diagonal \\(p\\)-permutation functors. Some parts of this work are joint with Boltje and Bouc.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>functorial equivalences<\/span><span>blocks<\/span><span>Donovan conjecture<\/span><span>Alperin’s weight conjecture<\/span><\/div>\n <\/div>\n <\/div>\n\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-schedule\">\n <div class=\"section-heading\">Programme<\/div>\n <p class=\"section-sub\">Talks are 50 minutes \u00b7 10-minute breaks between sessions<\/p>\n\n <div class=\"schedule-day-label\">Day 1 \u2014 Wednesday, June 18<\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">09:30<\/div><div class=\"sch-event\"><strong>Robert Boltje<\/strong> \u2014 On a conjecture of Feit <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">10:30<\/div><div class=\"sch-event\"><strong>\u0130pek Tuvay<\/strong> \u2014 Weight conjectures for Parker\u2013Semeraro fusion systems <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">11:30<\/div><div class=\"sch-event\"><strong>M. Yasir K\u0131zmaz<\/strong> \u2014 A generalization of the Alperin Fusion theorem <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">12:30<\/div><div class=\"sch-event\">Lunch Break <span class=\"sch-type break\">Break<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">14:30<\/div><div class=\"sch-event\"><strong>Ruslan M\u00fcsl\u00fcmov<\/strong> \u2014 A Categorical Decomposition of ℂ×-fibered p-biset Functors <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">15:30<\/div><div class=\"sch-event\"><strong>Nariel Monteiro<\/strong> \u2014 Links between character triples <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n\n <div class=\"schedule-day-label\">Day 2 \u2014 Thursday, June 19<\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">09:30<\/div><div class=\"sch-event\"><strong>Laurence Barker<\/strong> \u2014 The pointed fusion system of a block <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">10:30<\/div><div class=\"sch-event\"><strong>Deniz Y\u0131lmaz<\/strong> \u2014 Diagonal p-permutation functors <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">11:30<\/div><div class=\"sch-event\"><strong>Robert Boltje<\/strong> \u2014 On a conjecture of Feit (cont.) <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">12:30<\/div><div class=\"sch-event\">Lunch Break <span class=\"sch-type break\">Break<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">13:30<\/div><div class=\"sch-event\"><strong>M. Yasir K\u0131zmaz<\/strong> \u2014 Applications (cont.) <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">14:30<\/div><div class=\"sch-event\"><strong>Nariel Monteiro<\/strong> \u2014 Links between character triples <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">15:30<\/div><div class=\"sch-event\"><strong>Ruslan M\u00fcsl\u00fcmov<\/strong> \u2014 Categorical Decomposition (cont.) <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n\n <div class=\"schedule-day-label\">Day 3 \u2014 Friday, June 20<\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">09:30<\/div><div class=\"sch-event\"><strong>\u0130pek Tuvay<\/strong> \u2014 Weight conjectures for Parker\u2013Semeraro fusion systems <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">10:30<\/div><div class=\"sch-event\"><strong>Laurence Barker<\/strong> \u2014 The pointed fusion system of a block <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">11:30<\/div><div class=\"sch-event\"><strong>Deniz Y\u0131lmaz<\/strong> \u2014 Functorial equivalences between blocks of finite groups <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">12:30<\/div><div class=\"sch-event\">Closing & Farewell <span class=\"sch-type social\">Social<\/span><\/div><\/div>\n\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-gallery\">\n <div class=\"section-heading\">Photo Gallery<\/div>\n <div class=\"gallery-grid\">\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/bdf06095fa6c6f8dcd5d2abe2c1052bc-scaled.jpg\" alt=\"Opening session\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/2cd7f142d3fe02a2ce4a21d4444d9c77.jpg\" alt=\"Invited talk\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/523d3bd4ce01262acf6f279731b6e144.jpg\" alt=\"Discussions\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/34d0dc8004b5d0bc4038a8730c1ffa50.jpg\" alt=\"Social dinner\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/a2a7e57783bd8d10cb64f27049ce97d1-scaled.jpg\" alt=\"Q&A session\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/cb6699df8015a79ec416c7ccefba5c22.jpg\" alt=\"Baku\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n<\/div>\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-info\">\n <div class=\"section-heading\">Further Information<\/div>\n <p class=\"section-sub\">Venue, organisation, and contact details<\/p>\n <div class=\"info-two-col\">\n <div>\n <div class=\"info-block\">\n <h4>Venue<\/h4>\n <p>The workshop takes place at the <strong>Mathematics Research Center of ASOIU<\/strong> (Azerbaijan State Oil and Industry University), Baku, Azerbaijan.<\/p>\n <\/div>\n <div class=\"info-block\">\n <h4>Getting to Baku<\/h4>\n <ul>\n <li>International flights to Heydar Aliyev International Airport (GYD)<\/li>\n <li>Well connected from Istanbul, Moscow, Dubai, and major European hubs<\/li>\n <li>City centre easily reached by taxi or metro from the airport<\/li>\n <\/ul>\n <\/div>\n <div class=\"info-block\">\n <h4>About Baku<\/h4>\n <p>Baku is the capital of Azerbaijan, situated on the Caspian Sea. The city blends a UNESCO-listed medieval Old City with modern architecture, and hosts a vibrant mathematical community through institutions such as ASOIU and ADA University.<\/p>\n <\/div>\n <\/div>\n <div>\n <div class=\"info-block\">\n <h4>Organizer<\/h4>\n <div class=\"org-list\">\n <div class=\"org-person\">\n <strong>Mathematics Research Center<\/strong>\n <span>ASOIU \u2014 Azerbaijan State Oil and Industry University, Baku<\/span>\n <\/div>\n <\/div>\n <\/div>\n <div class=\"info-block\">\n <h4>Participants<\/h4>\n <p>The workshop features 7 invited talks by specialists from Bilkent University, UC Santa Cruz, ADA University, and Mimar Sinan Fine Arts University, covering fusion systems, block theory, biset functors, and character theory.<\/p>\n <\/div>\n <div class=\"info-block\">\n <h4>Contact<\/h4>\n <p>For enquiries about the workshop, please contact the Mathematics Research Center at ASOIU, Baku.<\/p>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n <\/div>\n\n <div class=\"conf-footer\">\n <span>FGTR 2025 \u00b7 Mathematics Research Center, ASOIU, Baku<\/span>\n <a href=\"#\">↑ Back to top<\/a>\n <\/div>\n\n<\/div>\n\n<div class=\"modal-overlay\" id=\"speaker-modal\">\n <div class=\"modal-box\">\n <div class=\"modal-header\">\n <div class=\"modal-avatar\" id=\"modal-avatar\">\u2014<\/div>\n <div>\n <div class=\"modal-name\" id=\"modal-name\">Speaker Name<\/div>\n <div class=\"modal-affil\" id=\"modal-affil\">Affiliation<\/div>\n <\/div>\n <button class=\"modal-close\" id=\"modal-close\">✕<\/button>\n <\/div>\n <div class=\"modal-body\" id=\"modal-body\"><p>Biography to be added.<\/p><\/div>\n <\/div>\n<\/div>\n\n<script>\n\/\/ Tab switching\ndocument.querySelectorAll('.conf-tab').forEach(tab => {\n tab.addEventListener('click', () => {\n const panel = tab.dataset.panel;\n document.querySelectorAll('.conf-tab').forEach(t => t.classList.remove('active'));\n document.querySelectorAll('.conf-panel').forEach(p => p.classList.remove('active'));\n tab.classList.add('active');\n document.getElementById('panel-' + panel).classList.add('active');\n });\n});\n\n\/\/ Abstract accordions\ndocument.querySelectorAll('[data-abstract]').forEach(title => {\n title.addEventListener('click', () => {\n const body = title.nextElementSibling.nextElementSibling;\n const arrow = title.querySelector('.toggle-arrow');\n const open = body.classList.toggle('open');\n arrow.style.transform = open ? 'rotate(180deg)' : '';\n });\n});\n\n\/\/ Speaker modal\nconst speakers = [\n { name: 'Laurence Barker', affil: 'Bilkent University', bio: 'Biography to be added.' },\n { name: 'Robert Boltje', affil: 'University of California, Santa Cruz', bio: 'Biography to be added.' },\n { name: 'M. Yasir K\u0131zmaz', affil: 'Bilkent University', bio: 'Biography to be added.' },\n { name: 'Nariel Monteiro', affil: 'University of California, Santa Cruz', bio: 'Biography to be added.' },\n { name: 'Ruslan M\u00fcsl\u00fcmov', affil: 'ADA University', bio: 'Biography to be added.' },\n { name: '\u0130pek Tuvay', affil: 'Mimar Sinan Fine Arts University', bio: 'Biography to be added.' },\n { name: 'Deniz Y\u0131lmaz', affil: 'Bilkent University', bio: 'Biography to be added.' }\n];\n\ndocument.querySelectorAll('.speaker-card').forEach(card => {\n card.addEventListener('click', () => {\n const idx = +card.dataset.speaker;\n const s = speakers[idx];\n document.getElementById('modal-avatar').textContent = s.name.split(' ').map(w => w[0]).join('').slice(0, 2);\n document.getElementById('modal-name').textContent = s.name;\n document.getElementById('modal-affil').textContent = s.affil;\n document.getElementById('modal-body').innerHTML = '<p>' + s.bio + '<\/p>';\n document.getElementById('speaker-modal').classList.add('open');\n });\n});\n\ndocument.getElementById('modal-close').addEventListener('click', () => {\n document.getElementById('speaker-modal').classList.remove('open');\n});\ndocument.getElementById('speaker-modal').addEventListener('click', e => {\n if (e.target === e.currentTarget) e.currentTarget.classList.remove('open');\n});\n<\/script>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>FGTR 2025 \u2014 Finite Groups and Their Representations Workshop \u00b7 Algebra \u00b7 Group Theory Finite Groups andTheir Representations FGTR 2025 \u00b7 Mathematics Research Center, ASOIU June 18\u201320, 2025 Baku, Azerbaijan FGTR 2025 Overview Invited Speakers Abstracts Schedule Gallery Further Info About the Workshop June 18\u201320, 2025 \u00b7 Baku, Azerbaijan This three-day workshop brings together researchers […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-208","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/comments?post=208"}],"version-history":[{"count":1,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/208\/revisions"}],"predecessor-version":[{"id":209,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/208\/revisions\/209"}],"wp:attachment":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/media?parent=208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":208,"date":"2026-04-15T14:43:27","date_gmt":"2026-04-15T14:43:27","guid":{"rendered":"https:\/\/mrc-baku.org\/?page_id=208"},"modified":"2026-04-15T14:45:18","modified_gmt":"2026-04-15T14:45:18","slug":"finite-groups-and-their-representations","status":"publish","type":"page","link":"https:\/\/mrc-baku.org\/index.php\/finite-groups-and-their-representations\/","title":{"rendered":"Finite Groups and Their Representations"},"content":{"rendered":"\n\n\n\n\n\nFGTR 2025 \u2014 Finite Groups and Their Representations<\/title>\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,600;1,400;1,500&family=DM+Mono:wght@300;400;500&family=Outfit:wght@300;400;500;600&display=swap\" rel=\"stylesheet\">\n<script>\nMathJax = { tex: { inlineMath: [['\\\\(','\\\\)']] } };\n<\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-chtml.js\" async><\/script>\n\n<style>\n:root {\n --cream: #F5F0E8;\n --ink: #1A1610;\n --rust: #B84A2F;\n --gold: #C99A2E;\n --slate: #3D4A5C;\n --mist: #E8EDF4;\n --rule: #C8BFA8;\n --garamond: 'EB Garamond', Georgia, serif;\n --mono: 'DM Mono', monospace;\n --sans: 'Outfit', sans-serif;\n}\n*, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }\nbody { background: #eee; padding: 2rem; font-family: var(--garamond); color: var(--ink); }\n\n.conf-block {\n max-width: 980px; margin: 0 auto; background: var(--cream);\n border: 1px solid var(--rule);\n box-shadow: 4px 4px 0 var(--rule), 8px 8px 0 #d8cdb8;\n overflow: hidden;\n}\n\n.conf-hero {\n background: var(--slate); color: var(--cream);\n padding: 3.5rem 3rem 2.5rem; position: relative; overflow: hidden;\n}\n.conf-hero::before {\n content: 'G S p B F R';\n position: absolute; top: -10px; right: -20px;\n font-family: var(--garamond); font-size: 9rem;\n letter-spacing: 0.05em; color: rgba(255,255,255,0.04);\n pointer-events: none; line-height: 1;\n}\n.conf-hero-tag {\n font-family: var(--mono); font-size: 0.7rem; letter-spacing: 0.18em;\n text-transform: uppercase; color: var(--gold); margin-bottom: 1rem;\n display: flex; align-items: center; gap: 0.5rem;\n}\n.conf-hero-tag::before { content: ''; display: inline-block; width: 24px; height: 1px; background: var(--gold); }\n.conf-title {\n font-family: var(--garamond); font-size: clamp(1.9rem, 4vw, 3rem);\n font-weight: 500; line-height: 1.15; margin-bottom: 0.7rem; letter-spacing: -0.01em;\n}\n.conf-subtitle {\n font-family: var(--garamond); font-style: italic; font-size: 1.1rem;\n color: rgba(245,240,232,0.7); margin-bottom: 1.8rem;\n}\n.conf-meta { display: flex; flex-wrap: wrap; gap: 1.5rem; font-family: var(--sans); font-size: 0.8rem; color: rgba(245,240,232,0.75); }\n.conf-meta span { display: flex; align-items: center; gap: 0.4rem; }\n.conf-meta svg { width: 13px; height: 13px; opacity: 0.7; }\n\n.conf-nav { display: flex; border-bottom: 1px solid var(--rule); background: #EDE8DE; overflow-x: auto; scrollbar-width: none; }\n.conf-nav::-webkit-scrollbar { display: none; }\n.conf-tab {\n padding: 0.9rem 1.4rem; font-family: var(--sans); font-size: 0.78rem;\n font-weight: 500; letter-spacing: 0.06em; text-transform: uppercase;\n cursor: pointer; border: none; background: none; color: #7A6E60;\n white-space: nowrap; border-bottom: 2px solid transparent; margin-bottom: -1px;\n transition: color 0.2s, border-color 0.2s;\n}\n.conf-tab:hover { color: var(--ink); }\n.conf-tab.active { color: var(--rust); border-bottom-color: var(--rust); }\n\n.conf-panels { padding: 2.5rem 3rem; }\n.conf-panel { display: none; }\n.conf-panel.active { display: block; }\n\n.section-heading {\n font-family: var(--garamond); font-size: 1.45rem; font-weight: 500;\n margin-bottom: 0.3rem; display: flex; align-items: center; gap: 0.7rem;\n}\n.section-heading::after { content: ''; flex: 1; height: 1px; background: var(--rule); }\n.section-sub { font-family: var(--garamond); font-style: italic; font-size: 0.92rem; color: #7A6E60; margin-bottom: 2rem; }\n\n.overview-grid { display: grid; grid-template-columns: 1fr 260px; gap: 2.5rem; }\n.overview-body { font-size: 1.05rem; line-height: 1.8; color: #2E2820; }\n.overview-body p + p { margin-top: 1em; }\n.info-card { background: var(--mist); border: 1px solid var(--rule); padding: 1.4rem 1.5rem; margin-bottom: 1rem; }\n.info-card-label { font-family: var(--mono); font-size: 0.65rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--rust); margin-bottom: 0.4rem; }\n.info-card-value { font-family: var(--sans); font-size: 0.88rem; color: var(--ink); line-height: 1.5; }\n\n.speakers-grid { display: grid; grid-template-columns: repeat(auto-fill, minmax(260px, 1fr)); gap: 1.5rem; }\n.speaker-card { border: 1px solid var(--rule); cursor: pointer; transition: box-shadow 0.2s, transform 0.2s; background: #fff; }\n.speaker-card:hover { box-shadow: 3px 3px 0 var(--rust); transform: translate(-1px,-1px); }\n.speaker-info { padding: 1.4rem 1.4rem 1.5rem; }\n.speaker-name { font-family: var(--garamond); font-size: 1.1rem; font-weight: 500; margin-bottom: 0.15rem; }\n.speaker-affil { font-family: var(--sans); font-size: 0.75rem; color: #7A6E60; margin-bottom: 0.6rem; }\n.speaker-topic { font-family: var(--garamond); font-style: italic; font-size: 0.88rem; color: var(--rust); line-height: 1.4; }\n.speaker-tag { display: inline-block; font-family: var(--mono); font-size: 0.6rem; letter-spacing: 0.1em; background: var(--mist); color: var(--slate); padding: 0.15rem 0.5rem; margin-top: 0.6rem; text-transform: uppercase; }\n\n.abstract-item { border-left: 3px solid var(--rule); padding: 0 0 0 1.5rem; margin-bottom: 2.2rem; transition: border-color 0.2s; }\n.abstract-item:hover { border-left-color: var(--rust); }\n.abstract-item:last-child { margin-bottom: 0; }\n.abstract-speaker { font-family: var(--sans); font-size: 0.72rem; font-weight: 500; letter-spacing: 0.1em; text-transform: uppercase; color: var(--slate); margin-bottom: 0.3rem; }\n.abstract-title { font-family: var(--garamond); font-size: 1.2rem; font-weight: 500; margin-bottom: 0.2rem; cursor: pointer; display: flex; align-items: baseline; justify-content: space-between; gap: 1rem; }\n.abstract-title .toggle-arrow { font-size: 0.75rem; color: var(--rust); flex-shrink: 0; transition: transform 0.25s; }\n.abstract-meta { font-family: var(--mono); font-size: 0.67rem; color: #9A8E80; letter-spacing: 0.05em; margin-bottom: 0.6rem; }\n.abstract-body { font-size: 0.97rem; line-height: 1.75; color: #2E2820; max-height: 0; overflow: hidden; transition: max-height 0.4s ease; }\n.abstract-body.open { max-height: 800px; }\n.abstract-body p { margin-top: 0.5em; }\n.abstract-keywords { margin-top: 0.8em; font-family: var(--mono); font-size: 0.68rem; color: var(--slate); letter-spacing: 0.04em; }\n.abstract-keywords span { display: inline-block; background: var(--mist); padding: 0.1rem 0.5rem; margin: 0.1rem 0.2rem 0 0; }\n\n.schedule-day-label { font-family: var(--mono); font-size: 0.68rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--rust); margin: 2rem 0 0.8rem; display: flex; align-items: center; gap: 0.7rem; }\n.schedule-day-label::after { content: ''; flex: 1; height: 1px; background: var(--rule); }\n.schedule-day-label:first-child { margin-top: 0; }\n.schedule-row { display: grid; grid-template-columns: 90px 1fr; gap: 0 1.5rem; padding: 0.7rem 0; border-bottom: 1px solid #e8e0d0; align-items: start; }\n.schedule-row:last-child { border-bottom: none; }\n.sch-time { font-family: var(--mono); font-size: 0.75rem; color: #7A6E60; padding-top: 0.1rem; letter-spacing: 0.03em; }\n.sch-event { font-size: 0.97rem; line-height: 1.5; }\n.sch-type { display: inline-block; font-family: var(--mono); font-size: 0.6rem; letter-spacing: 0.1em; padding: 0.1rem 0.45rem; text-transform: uppercase; margin-left: 0.5rem; vertical-align: middle; }\n.sch-type.talk { background: #EDF2FA; color: var(--slate); }\n.sch-type.social { background: #FBF0E6; color: #9A5020; }\n.sch-type.break { background: #F0F0F0; color: #888; }\n\n.gallery-intro { font-family: var(--garamond); font-style: italic; font-size: 0.95rem; color: #7A6E60; margin-bottom: 1.5rem; line-height: 1.6; }\n.gallery-grid { display: grid; grid-template-columns: repeat(3, 1fr); gap: 6px; }\n.gallery-cell { aspect-ratio: 4\/3; background: var(--mist); display: flex; align-items: center; justify-content: center; overflow: hidden; cursor: zoom-in; }\n.gallery-cell:first-child { grid-column: span 2; aspect-ratio: 16\/9; }\n.gallery-cell-inner { width: 100%; height: 100%; display: flex; flex-direction: column; align-items: center; justify-content: center; gap: 0.5rem; background: linear-gradient(135deg, #dce4f0 0%, #c8d4e6 50%, #b8c8e0 100%); transition: transform 0.3s; }\n.gallery-cell:hover .gallery-cell-inner { transform: scale(1.03); }\n.gallery-cell-inner .icon { font-size: 2.2rem; opacity: 0.35; }\n.gallery-cell-inner .caption { font-family: var(--sans); font-size: 0.65rem; letter-spacing: 0.06em; text-transform: uppercase; color: var(--slate); opacity: 0.7; }\n.gallery-upload-note { margin-top: 1rem; font-family: var(--mono); font-size: 0.7rem; color: #9A8E80; letter-spacing: 0.04em; text-align: center; padding: 0.8rem; border: 1px dashed var(--rule); }\n\n.info-two-col { display: grid; grid-template-columns: 1fr 1fr; gap: 2rem; }\n.info-block { margin-bottom: 2rem; }\n.info-block h4 { font-family: var(--garamond); font-size: 1.05rem; font-weight: 500; margin-bottom: 0.5rem; border-bottom: 1px solid var(--rule); padding-bottom: 0.3rem; }\n.info-block p, .info-block li { font-family: var(--garamond); font-size: 0.95rem; line-height: 1.7; color: #2E2820; }\n.info-block ul { list-style: none; padding: 0; }\n.info-block ul li::before { content: '\u2192 '; color: var(--rust); font-family: var(--mono); }\n.org-list { display: flex; flex-direction: column; gap: 0.6rem; margin-top: 0.5rem; }\n.org-person { display: flex; flex-direction: column; }\n.org-person strong { font-family: var(--sans); font-size: 0.82rem; font-weight: 500; }\n.org-person span { font-family: var(--garamond); font-style: italic; font-size: 0.82rem; color: #7A6E60; }\n\n.conf-footer { background: var(--ink); color: rgba(245,240,232,0.5); font-family: var(--mono); font-size: 0.65rem; letter-spacing: 0.06em; padding: 1rem 3rem; display: flex; align-items: center; justify-content: space-between; }\n.conf-footer a { color: var(--gold); text-decoration: none; }\n\n.modal-overlay { display: none; position: fixed; inset: 0; background: rgba(26,22,16,0.7); z-index: 1000; align-items: center; justify-content: center; padding: 2rem; }\n.modal-overlay.open { display: flex; }\n.modal-box { background: var(--cream); max-width: 560px; width: 100%; max-height: 80vh; overflow-y: auto; border: 1px solid var(--rule); box-shadow: 8px 8px 0 rgba(26,22,16,0.25); }\n.modal-header { display: flex; align-items: center; gap: 1rem; padding: 1.5rem; border-bottom: 1px solid var(--rule); background: var(--slate); color: var(--cream); }\n.modal-avatar { width: 64px; height: 64px; border-radius: 50%; background: linear-gradient(135deg, #d8e0ec, #b8c8e0); display: flex; align-items: center; justify-content: center; font-size: 1.4rem; flex-shrink: 0; font-family: var(--garamond); color: var(--slate); font-weight: 500; }\n.modal-name { font-family: var(--garamond); font-size: 1.3rem; font-weight: 500; }\n.modal-affil { font-family: var(--sans); font-size: 0.75rem; color: rgba(245,240,232,0.65); }\n.modal-body { padding: 1.5rem; }\n.modal-body p { font-size: 0.97rem; line-height: 1.75; color: #2E2820; }\n.modal-close { background: none; border: none; cursor: pointer; color: var(--cream); font-size: 1.4rem; margin-left: auto; line-height: 1; padding: 0.2rem; opacity: 0.6; transition: opacity 0.2s; }\n.modal-close:hover { opacity: 1; }\n\n@media (max-width: 680px) {\n .overview-grid { grid-template-columns: 1fr; }\n .conf-panels { padding: 2rem 1.5rem; }\n .info-two-col { grid-template-columns: 1fr; }\n .gallery-grid { grid-template-columns: repeat(2,1fr); }\n}\n::-webkit-scrollbar { width: 5px; height: 5px; }\n::-webkit-scrollbar-track { background: transparent; }\n::-webkit-scrollbar-thumb { background: var(--rule); border-radius: 3px; }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"conf-block\" id=\"conf-block-fgtr2025\">\n\n <div class=\"conf-hero\">\n <div class=\"conf-hero-tag\">Workshop \u00b7 Algebra \u00b7 Group Theory<\/div>\n <h1 class=\"conf-title\">Finite Groups and<br>Their Representations<\/h1>\n <p class=\"conf-subtitle\">FGTR 2025 \u00b7 Mathematics Research Center, ASOIU<\/p>\n <div class=\"conf-meta\">\n <span>\n <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 1a5 5 0 100 10A5 5 0 008 1zM0 8a8 8 0 1116 0A8 8 0 010 8z\"\/><path d=\"M7.5 4.5v4l2.5 1.5.5-.87L8.5 8V4.5z\"\/><\/svg>\n June 18\u201320, 2025\n <\/span>\n <span>\n <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 0C5.24 0 3 2.24 3 5c0 3.75 5 11 5 11s5-7.25 5-11c0-2.76-2.24-5-5-5zm0 7.5a2.5 2.5 0 110-5 2.5 2.5 0 010 5z\"\/><\/svg>\n Baku, Azerbaijan\n <\/span>\n <span>\n <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M7 0H2a1 1 0 00-1 1v2h14V1a1 1 0 00-1-1H7zm7 4H1v10a1 1 0 001 1h12a1 1 0 001-1V4z\"\/><\/svg>\n FGTR 2025\n <\/span>\n <\/div>\n <\/div>\n\n <nav class=\"conf-nav\" role=\"tablist\">\n <button class=\"conf-tab active\" data-panel=\"overview\" role=\"tab\">Overview<\/button>\n <button class=\"conf-tab\" data-panel=\"speakers\" role=\"tab\">Invited Speakers<\/button>\n <button class=\"conf-tab\" data-panel=\"abstracts\" role=\"tab\">Abstracts<\/button>\n <button class=\"conf-tab\" data-panel=\"schedule\" role=\"tab\">Schedule<\/button>\n <button class=\"conf-tab\" data-panel=\"gallery\" role=\"tab\">Gallery<\/button>\n <button class=\"conf-tab\" data-panel=\"info\" role=\"tab\">Further Info<\/button>\n <\/nav>\n\n <div class=\"conf-panels\">\n\n <section class=\"conf-panel active\" id=\"panel-overview\">\n <div class=\"section-heading\">About the Workshop<\/div>\n <p class=\"section-sub\">June 18\u201320, 2025 \u00b7 Baku, Azerbaijan<\/p>\n <div class=\"overview-grid\">\n <div class=\"overview-body\">\n <p>This three-day workshop brings together researchers working in the theory of finite groups and their representations, with a particular focus on fusion systems, block theory, biset functors, and character-theoretic methods.<\/p>\n <p>The programme features seven invited talks by leading specialists from Turkey, the United States, and Azerbaijan, covering topics ranging from the Alperin\u2013McKay conjecture and Feit’s conjecture to categorical decompositions of biset functors and weight conjectures for exotic fusion systems.<\/p>\n <p>The workshop is organized by the <em>Mathematics Research Center of ASOIU<\/em> (Azerbaijan State Oil and Industry University), Baku.<\/p>\n <\/div>\n <div class=\"overview-sidebar\">\n <div class=\"info-card\"><div class=\"info-card-label\">Dates<\/div><div class=\"info-card-value\">June 18\u201320, 2025<\/div><\/div>\n <div class=\"info-card\"><div class=\"info-card-label\">Venue<\/div><div class=\"info-card-value\">Mathematics Research Center<br>ASOIU, Baku, Azerbaijan<\/div><\/div>\n <div class=\"info-card\"><div class=\"info-card-label\">Format<\/div><div class=\"info-card-value\">In-person<\/div><\/div>\n <\/div>\n <\/div>\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-speakers\">\n <div class=\"section-heading\">Invited Speakers<\/div>\n <p class=\"section-sub\">Click a card to view biography<\/p>\n <div class=\"speakers-grid\">\n <div class=\"speaker-card\" data-speaker=\"0\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Laurence Barker<\/div>\n <div class=\"speaker-affil\">Bilkent University<\/div>\n <div class=\"speaker-topic\">The pointed fusion system of a block<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"1\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Robert Boltje<\/div>\n <div class=\"speaker-affil\">University of California, Santa Cruz<\/div>\n <div class=\"speaker-topic\">On a conjecture of Feit<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"2\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">M. Yasir K\u0131zmaz<\/div>\n <div class=\"speaker-affil\">Bilkent University<\/div>\n <div class=\"speaker-topic\">A generalization of the Alperin Fusion theorem and its applications<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"3\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Nariel Monteiro<\/div>\n <div class=\"speaker-affil\">University of California, Santa Cruz<\/div>\n <div class=\"speaker-topic\">Links between character triples<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"4\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Ruslan M\u00fcsl\u00fcmov<\/div>\n <div class=\"speaker-affil\">ADA University<\/div>\n <div class=\"speaker-topic\">A Categorical Decomposition of ℂ×-fibered <i>p<\/i>-biset Functors<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"5\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">\u0130pek Tuvay<\/div>\n <div class=\"speaker-affil\">Mimar Sinan Fine Arts University<\/div>\n <div class=\"speaker-topic\">Weight conjectures for Parker\u2013Semeraro fusion systems<\/div>\n <\/div>\n <\/div>\n <div class=\"speaker-card\" data-speaker=\"6\">\n <div class=\"speaker-info\">\n <div class=\"speaker-name\">Deniz Y\u0131lmaz<\/div>\n <div class=\"speaker-affil\">Bilkent University<\/div>\n <div class=\"speaker-topic\">Diagonal <i>p<\/i>-permutation functors \u00b7 Functorial equivalences between blocks<\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-abstracts\">\n <div class=\"section-heading\">Abstracts<\/div>\n <p class=\"section-sub\">Click a title to expand the abstract<\/p>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Laurence Barker \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>The pointed fusion system of a block<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Thursday, June 19 \u00b7 09:30<\/div>\n <div class=\"abstract-body\">\n <p>The pointed fusion system of a block is a category and a poset that refines the fusion system. Like the fusion system, it is a local invariant in that it is determined by the source algebra. Unlike the fusion system, it determines the number of simple modules. We shall show that it satisfies a generalization of the saturation condition. If it could be argued that mysterious invariants might be needed to cut inroads to the outstanding conjectures of block theory, then the pointed fusion system fits the bill: we do not know whether it coincides with what Th\u00e9venaz called the Puig category.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>fusion systems<\/span><span>block theory<\/span><span>source algebra<\/span><span>Puig category<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Robert Boltje \u00b7 University of California, Santa Cruz<\/div>\n <div class=\"abstract-title\" data-abstract>On a conjecture of Feit<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Wednesday, June 18 \u00b7 09:30<\/div>\n <div class=\"abstract-body\">\n <p>In 1979, Walter Feit suggested to use the classification of finite simple groups to decide if the following statement holds: If \\(\\chi\\) is an irreducible character of a finite group \\(G\\) and if \\(n\\) is the smallest positive integer such that all values of \\(\\chi\\) belong to the \\(n\\)-th cyclotomic field then \\(G\\) has an element of order \\(n\\). In 1986, Ferguson\u2013Turull and Amit\u2013Chillag proved independently that this holds if \\(G\\) is solvable. Not much progress has been made in the following years. Only recently, in joint work with A. Kleshchev, G. Navarro, and Ph. H. Tiep, we showed that the answer is yes, provided that every non-abelian finite simple group satisfies a condition that we call the inductive Feit condition. This talk describes the reduction theorem and other related results and conjectures.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>Feit conjecture<\/span><span>irreducible characters<\/span><span>cyclotomic fields<\/span><span>finite simple groups<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">M. Yasir K\u0131zmaz \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>A generalization of the Alperin Fusion theorem and its applications<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Wednesday, June 18 \u00b7 11:30<\/div>\n <div class=\"abstract-body\">\n <p>In this talk, we aim to present a generalization of the Alperin\u2013Goldschmidt fusion theorem for saturated fusion systems. Our approach introduces the notion of \\(\\mathcal{F}\\)-essential subgroups relative to a strongly \\(\\mathcal{F}\\)-closed subgroup \\(P\\) of a \\(p\\)-group \\(S\\). We show that any \\(\\mathcal{F}\\)-isomorphism between subgroups of \\(P\\) can be decomposed using some automorphisms of \\(P\\) and these relative \\(\\mathcal{F}\\)-essential subgroups. When \\(P\\) is taken to be equal to \\(S\\), the Alperin\u2013Goldschmidt fusion theorem can be obtained as a special case.<\/p>\n <p>A \\(p\\)-group \\(P\\) is strongly resistant in saturated fusion systems if \\(P \\unlhd \\mathcal{F}\\) whenever there is an over \\(p\\)-group \\(S\\) and a saturated fusion system \\(\\mathcal{F}\\) on \\(S\\) such that \\(P\\) is strongly \\(\\mathcal{F}\\)-closed. We show that several classes of \\(p\\)-groups are strongly resistant. We also give a new necessary and sufficient criterion for a strongly \\(\\mathcal{F}\\)-closed subgroup to be normal in \\(\\mathcal{F}\\). These results are obtained as a consequence of developing a theory of quasi and semi-saturated fusion systems, which seems to be interesting in its own right.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>Alperin\u2013Goldschmidt theorem<\/span><span>saturated fusion systems<\/span><span>essential subgroups<\/span><span>strongly closed<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Nariel Monteiro \u00b7 University of California, Santa Cruz<\/div>\n <div class=\"abstract-title\" data-abstract>Links between character triples<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Thursday, June 19 \u00b7 14:30<\/div>\n <div class=\"abstract-body\">\n <p>We will introduce the notion of a link between character triples. The motivation to consider this notion has multiple reasons. Firstly, links between character triples induce special character triple isomorphisms. This provides a new perspective for isomorphisms between character triples and a different conceptual understanding. Secondly, links between character triples provide equivalent reformulations of complicated conditions (involving projective representations) that play a fundamental role in the reductions of the McKay conjecture and the Feit conjecture to finite simple groups. This is joint work with Robert Boltje and John Revere McHugh.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>character triples<\/span><span>McKay conjecture<\/span><span>projective representations<\/span><span>finite simple groups<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Ruslan M\u00fcsl\u00fcmov \u00b7 ADA University<\/div>\n <div class=\"abstract-title\" data-abstract>A Categorical Decomposition of ℂ×-fibered p-biset Functors<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Wednesday, June 18 \u00b7 14:30<\/div>\n <div class=\"abstract-body\">\n <p>We generalize Bouc’s construction of orthogonal idempotents in the double Burnside algebra to the setting of the double \\(\\mathbb{C}^\\times\\)-fibered Burnside algebra. This yields a structural decomposition of the evaluations of \\(\\mathbb{C}^\\times\\)-fibered biset functors on finite groups. We then construct a complete set of orthogonal idempotents in the category of \\(\\mathbb{C}^\\times\\)-fibered \\(p\\)-biset functors, leading to a categorical decomposition of this category into subcategories indexed by isomorphism classes of atoric \\(p\\)-groups. Furthermore, we introduce the notion of <em>vertices<\/em> for indecomposable functors and establish that the \\(\\mathrm{Ext}\\)-groups between simple functors with distinct vertices vanish. As an application, we describe a set containing composition factors of the monomial Burnside functor, thereby providing new insights into its structure. Additionally, we develop a technique for analyzing fibered biset functors via their underlying biset structures. This is a joint work with Olcay Co\u015fkun.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>biset functors<\/span><span>Burnside algebra<\/span><span>orthogonal idempotents<\/span><span>p-groups<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">\u0130pek Tuvay \u00b7 Mimar Sinan Fine Arts University<\/div>\n <div class=\"abstract-title\" data-abstract>Weight conjectures for Parker\u2013Semeraro fusion systems<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Friday, June 20 \u00b7 09:30<\/div>\n <div class=\"abstract-body\">\n <p>Weight conjectures for fusion systems are conjectural statements for fusion systems which are motivated by local-global conjectures in block theory and were put forward by Kessar, Linckelmann, Lynd and Semeraro in 2019. In fact, the interest in weight conjectures goes beyond the local-global conjectures from block theory. They apply equally well in the situation where the fusion system is block-exotic. In the first part of the talk, I will introduce these conjectures and mention their link to conjectures in block theory. Then I will present the results which verify these conjectures for the family of Parker\u2013Semeraro fusion systems which contains 27 block-exotic fusion systems. This is a joint work with Kessar, Semeraro and Serwene.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>weight conjectures<\/span><span>Parker\u2013Semeraro systems<\/span><span>block-exotic fusion systems<\/span><span>block theory<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Deniz Y\u0131lmaz \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>Diagonal p-permutation functors<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Thursday, June 19 \u00b7 10:30<\/div>\n <div class=\"abstract-body\">\n <p>Let \\(p\\) be a prime number and let \\(\\mathbb{F}\\) be an algebraically closed field of characteristic \\(0\\) or \\(p\\). In this talk we introduce the notion of diagonal \\(p\\)-permutation functors over \\(\\mathbb{F}\\). We show that the simple diagonal \\(p\\)-permutation functors \\(S_{L,u,V}\\) are parametrized by triples \\((L,u,V)\\) where \\(L\\) is a \\(p\\)-group, \\(u\\) is a \\(p’\\)-automorphism of \\(L\\) and \\(V\\) is a simple \\(\\mathbb{F}\\mathrm{Out}(L,u)\\)-module. We also describe the evaluations of the simple functors. In particular, if \\(\\mathbb{F}\\) has characteristic \\(p\\), we show that for a finite group \\(G\\), the dimension of \\(S_{L,1,\\mathbb{F}}(G)\\) is equal to the number of conjugacy classes of \\(p\\)-regular elements of \\(G\\) with defect isomorphic to \\(L\\). We finally prove that if \\(\\mathbb{F}\\) is of characteristic zero, then the category of diagonal \\(p\\)-permutation functors is semisimple. This is a joint work with Bouc.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>p-permutation functors<\/span><span>simple functors<\/span><span>p-groups<\/span><span>semisimple category<\/span><\/div>\n <\/div>\n <\/div>\n\n <div class=\"abstract-item\">\n <div class=\"abstract-speaker\">Deniz Y\u0131lmaz \u00b7 Bilkent University<\/div>\n <div class=\"abstract-title\" data-abstract>Functorial equivalences between blocks of finite groups<span class=\"toggle-arrow\">\u25be<\/span><\/div>\n <div class=\"abstract-meta\">Invited Talk \u00b7 Friday, June 20 \u00b7 10:30<\/div>\n <div class=\"abstract-body\">\n <p>We will talk about the notion of functorial equivalences between blocks of finite groups, a notion introduced using the theory of diagonal \\(p\\)-permutation functors. We investigate the invariants preserved by functorial equivalences and their relations with other well-studied equivalences. We prove a finiteness theorem in the spirit of Donovan’s and Puig’s finiteness conjectures: there are only finitely many blocks of finite groups with a given defect group, up to functorial equivalence. We also give a reformulation of Alperin’s weight conjecture in terms of diagonal \\(p\\)-permutation functors. Some parts of this work are joint with Boltje and Bouc.<\/p>\n <div class=\"abstract-keywords\">Keywords: <span>functorial equivalences<\/span><span>blocks<\/span><span>Donovan conjecture<\/span><span>Alperin’s weight conjecture<\/span><\/div>\n <\/div>\n <\/div>\n\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-schedule\">\n <div class=\"section-heading\">Programme<\/div>\n <p class=\"section-sub\">Talks are 50 minutes \u00b7 10-minute breaks between sessions<\/p>\n\n <div class=\"schedule-day-label\">Day 1 \u2014 Wednesday, June 18<\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">09:30<\/div><div class=\"sch-event\"><strong>Robert Boltje<\/strong> \u2014 On a conjecture of Feit <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">10:30<\/div><div class=\"sch-event\"><strong>\u0130pek Tuvay<\/strong> \u2014 Weight conjectures for Parker\u2013Semeraro fusion systems <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">11:30<\/div><div class=\"sch-event\"><strong>M. Yasir K\u0131zmaz<\/strong> \u2014 A generalization of the Alperin Fusion theorem <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">12:30<\/div><div class=\"sch-event\">Lunch Break <span class=\"sch-type break\">Break<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">14:30<\/div><div class=\"sch-event\"><strong>Ruslan M\u00fcsl\u00fcmov<\/strong> \u2014 A Categorical Decomposition of ℂ×-fibered p-biset Functors <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">15:30<\/div><div class=\"sch-event\"><strong>Nariel Monteiro<\/strong> \u2014 Links between character triples <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n\n <div class=\"schedule-day-label\">Day 2 \u2014 Thursday, June 19<\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">09:30<\/div><div class=\"sch-event\"><strong>Laurence Barker<\/strong> \u2014 The pointed fusion system of a block <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">10:30<\/div><div class=\"sch-event\"><strong>Deniz Y\u0131lmaz<\/strong> \u2014 Diagonal p-permutation functors <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">11:30<\/div><div class=\"sch-event\"><strong>Robert Boltje<\/strong> \u2014 On a conjecture of Feit (cont.) <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">12:30<\/div><div class=\"sch-event\">Lunch Break <span class=\"sch-type break\">Break<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">13:30<\/div><div class=\"sch-event\"><strong>M. Yasir K\u0131zmaz<\/strong> \u2014 Applications (cont.) <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">14:30<\/div><div class=\"sch-event\"><strong>Nariel Monteiro<\/strong> \u2014 Links between character triples <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">15:30<\/div><div class=\"sch-event\"><strong>Ruslan M\u00fcsl\u00fcmov<\/strong> \u2014 Categorical Decomposition (cont.) <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n\n <div class=\"schedule-day-label\">Day 3 \u2014 Friday, June 20<\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">09:30<\/div><div class=\"sch-event\"><strong>\u0130pek Tuvay<\/strong> \u2014 Weight conjectures for Parker\u2013Semeraro fusion systems <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">10:30<\/div><div class=\"sch-event\"><strong>Laurence Barker<\/strong> \u2014 The pointed fusion system of a block <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">11:30<\/div><div class=\"sch-event\"><strong>Deniz Y\u0131lmaz<\/strong> \u2014 Functorial equivalences between blocks of finite groups <span class=\"sch-type talk\">Talk<\/span><\/div><\/div>\n <div class=\"schedule-row\"><div class=\"sch-time\">12:30<\/div><div class=\"sch-event\">Closing & Farewell <span class=\"sch-type social\">Social<\/span><\/div><\/div>\n\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-gallery\">\n <div class=\"section-heading\">Photo Gallery<\/div>\n <div class=\"gallery-grid\">\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/bdf06095fa6c6f8dcd5d2abe2c1052bc-scaled.jpg\" alt=\"Opening session\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/2cd7f142d3fe02a2ce4a21d4444d9c77.jpg\" alt=\"Invited talk\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/523d3bd4ce01262acf6f279731b6e144.jpg\" alt=\"Discussions\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/34d0dc8004b5d0bc4038a8730c1ffa50.jpg\" alt=\"Social dinner\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/a2a7e57783bd8d10cb64f27049ce97d1-scaled.jpg\" alt=\"Q&A session\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n\n <div class=\"gallery-cell\">\n <img decoding=\"async\" src=\"http:\/\/mrc-baku.org\/wp-content\/uploads\/2025\/06\/cb6699df8015a79ec416c7ccefba5c22.jpg\" alt=\"Baku\" style=\"width:100%;height:100%;object-fit:cover;display:block;\">\n <\/div>\n<\/div>\n <\/section>\n\n <section class=\"conf-panel\" id=\"panel-info\">\n <div class=\"section-heading\">Further Information<\/div>\n <p class=\"section-sub\">Venue, organisation, and contact details<\/p>\n <div class=\"info-two-col\">\n <div>\n <div class=\"info-block\">\n <h4>Venue<\/h4>\n <p>The workshop takes place at the <strong>Mathematics Research Center of ASOIU<\/strong> (Azerbaijan State Oil and Industry University), Baku, Azerbaijan.<\/p>\n <\/div>\n <div class=\"info-block\">\n <h4>Getting to Baku<\/h4>\n <ul>\n <li>International flights to Heydar Aliyev International Airport (GYD)<\/li>\n <li>Well connected from Istanbul, Moscow, Dubai, and major European hubs<\/li>\n <li>City centre easily reached by taxi or metro from the airport<\/li>\n <\/ul>\n <\/div>\n <div class=\"info-block\">\n <h4>About Baku<\/h4>\n <p>Baku is the capital of Azerbaijan, situated on the Caspian Sea. The city blends a UNESCO-listed medieval Old City with modern architecture, and hosts a vibrant mathematical community through institutions such as ASOIU and ADA University.<\/p>\n <\/div>\n <\/div>\n <div>\n <div class=\"info-block\">\n <h4>Organizer<\/h4>\n <div class=\"org-list\">\n <div class=\"org-person\">\n <strong>Mathematics Research Center<\/strong>\n <span>ASOIU \u2014 Azerbaijan State Oil and Industry University, Baku<\/span>\n <\/div>\n <\/div>\n <\/div>\n <div class=\"info-block\">\n <h4>Participants<\/h4>\n <p>The workshop features 7 invited talks by specialists from Bilkent University, UC Santa Cruz, ADA University, and Mimar Sinan Fine Arts University, covering fusion systems, block theory, biset functors, and character theory.<\/p>\n <\/div>\n <div class=\"info-block\">\n <h4>Contact<\/h4>\n <p>For enquiries about the workshop, please contact the Mathematics Research Center at ASOIU, Baku.<\/p>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n <\/div>\n\n <div class=\"conf-footer\">\n <span>FGTR 2025 \u00b7 Mathematics Research Center, ASOIU, Baku<\/span>\n <a href=\"#\">↑ Back to top<\/a>\n <\/div>\n\n<\/div>\n\n<div class=\"modal-overlay\" id=\"speaker-modal\">\n <div class=\"modal-box\">\n <div class=\"modal-header\">\n <div class=\"modal-avatar\" id=\"modal-avatar\">\u2014<\/div>\n <div>\n <div class=\"modal-name\" id=\"modal-name\">Speaker Name<\/div>\n <div class=\"modal-affil\" id=\"modal-affil\">Affiliation<\/div>\n <\/div>\n <button class=\"modal-close\" id=\"modal-close\">✕<\/button>\n <\/div>\n <div class=\"modal-body\" id=\"modal-body\"><p>Biography to be added.<\/p><\/div>\n <\/div>\n<\/div>\n\n<script>\n\/\/ Tab switching\ndocument.querySelectorAll('.conf-tab').forEach(tab => {\n tab.addEventListener('click', () => {\n const panel = tab.dataset.panel;\n document.querySelectorAll('.conf-tab').forEach(t => t.classList.remove('active'));\n document.querySelectorAll('.conf-panel').forEach(p => p.classList.remove('active'));\n tab.classList.add('active');\n document.getElementById('panel-' + panel).classList.add('active');\n });\n});\n\n\/\/ Abstract accordions\ndocument.querySelectorAll('[data-abstract]').forEach(title => {\n title.addEventListener('click', () => {\n const body = title.nextElementSibling.nextElementSibling;\n const arrow = title.querySelector('.toggle-arrow');\n const open = body.classList.toggle('open');\n arrow.style.transform = open ? 'rotate(180deg)' : '';\n });\n});\n\n\/\/ Speaker modal\nconst speakers = [\n { name: 'Laurence Barker', affil: 'Bilkent University', bio: 'Biography to be added.' },\n { name: 'Robert Boltje', affil: 'University of California, Santa Cruz', bio: 'Biography to be added.' },\n { name: 'M. Yasir K\u0131zmaz', affil: 'Bilkent University', bio: 'Biography to be added.' },\n { name: 'Nariel Monteiro', affil: 'University of California, Santa Cruz', bio: 'Biography to be added.' },\n { name: 'Ruslan M\u00fcsl\u00fcmov', affil: 'ADA University', bio: 'Biography to be added.' },\n { name: '\u0130pek Tuvay', affil: 'Mimar Sinan Fine Arts University', bio: 'Biography to be added.' },\n { name: 'Deniz Y\u0131lmaz', affil: 'Bilkent University', bio: 'Biography to be added.' }\n];\n\ndocument.querySelectorAll('.speaker-card').forEach(card => {\n card.addEventListener('click', () => {\n const idx = +card.dataset.speaker;\n const s = speakers[idx];\n document.getElementById('modal-avatar').textContent = s.name.split(' ').map(w => w[0]).join('').slice(0, 2);\n document.getElementById('modal-name').textContent = s.name;\n document.getElementById('modal-affil').textContent = s.affil;\n document.getElementById('modal-body').innerHTML = '<p>' + s.bio + '<\/p>';\n document.getElementById('speaker-modal').classList.add('open');\n });\n});\n\ndocument.getElementById('modal-close').addEventListener('click', () => {\n document.getElementById('speaker-modal').classList.remove('open');\n});\ndocument.getElementById('speaker-modal').addEventListener('click', e => {\n if (e.target === e.currentTarget) e.currentTarget.classList.remove('open');\n});\n<\/script>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>FGTR 2025 \u2014 Finite Groups and Their Representations Workshop \u00b7 Algebra \u00b7 Group Theory Finite Groups andTheir Representations FGTR 2025 \u00b7 Mathematics Research Center, ASOIU June 18\u201320, 2025 Baku, Azerbaijan FGTR 2025 Overview Invited Speakers Abstracts Schedule Gallery Further Info About the Workshop June 18\u201320, 2025 \u00b7 Baku, Azerbaijan This three-day workshop brings together researchers […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-208","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/comments?post=208"}],"version-history":[{"count":1,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/208\/revisions"}],"predecessor-version":[{"id":209,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/208\/revisions\/209"}],"wp:attachment":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/media?parent=208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}