BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bob Olivier (Université Sorbonne Paris Nord) DTSTART:20260529T150000Z DTEND:20260529T161500Z DTSTAMP:20260423T021356Z UID:CIRGET/164 DESCRIPTION:Title: The local structure of finite groups and of their classifying spaces\ nby Bob Olivier (Université Sorbonne Paris Nord) as part of CRM - Sémina ire du CIRGET / Géométrie et Topologie\n\nInteractive livestream: https: //uqam.zoom.us/j/88383789249\nLecture held in PK-5115.\n\nAbstract\nFix a prime ${p}$. We say that two finite groups $G$ and\n$H$ are ``${p}$-equiva lent'' if there is an isomorphism between\nSylow $p$-subgroups $S \\in Syl _p(G)$ and $T\\in \nSyl_p({H})$ that preserves all $G-$ and\n${H}-$conjuga cy relations among elements and subgroups of $S$\nand $T$. We say that two topological spaces ${X}$ and ${Y}$ are ``${p}$-equivalent'' if there is a third space ${Z}$\, and maps $X\\to Z \\leftarrow Y$ that induce isomorph isms in homology\nwith coefficients in $\\mathbb{Z}/p$. (Both of these are equivalence\nrelations.) The main theorem I want to describe says that fi nite groups ${G}$ and ${H}$ are\n$p$-equivalent (as groups) if and only if their classifying spaces\nare ${p}$-equivalent (as spaces).\n\n\nI will s tart by defining in more detail classifying spaces of discrete\ngroups and the two kinds of ${p}$-equivalence described above\, and\nalso saying a l ittle about the background of the theorem. I then plan to\ngive some examp les of finite groups that are ${p}$-locally equivalent\nbut not isomorphic \, and say something about ideas that went into the\nproof of the theorem (carried out by several different people over a\nperiod of 10--15 years).\ n LOCATION:https://researchseminars.org/talk/CIRGET/164/ URL:https://uqam.zoom.us/j/88383789249 END:VEVENT END:VCALENDAR