BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pilar Páez Guillán (Vienna) DTSTART:20230110T140000Z DTEND:20230110T160000Z DTSTAMP:20260423T023017Z UID:WienGAGT/30 DESCRIPTION:Title: Counterexamples to the Zassenhaus conjecture on simple modular Lie algeb ras\nby Pilar Páez Guillán (Vienna) as part of Vienna Geometry and A nalysis on Groups Seminar\n\n\nAbstract\nHistorically\, the study of the ( outer) automorphism group of a given group (free\, simple...) has interest ed group-theorists\, topologists and geometers\, and consequently it is al so of great importance in the Lie algebra theory. In this talk\, we will b riefly revise some of the connections between groups and Lie algebras befo re giving a quick overview of the simple Lie algebras of classical and Car tan type over fields of positive characteristic. After that\, we will comp are the Schreier and Zassenhaus conjectures on the solvability of \\(\\mat hrm{Out}(G)\\) (resp. \\(\\mathrm{Out}(L)\\))\, the group of outer automor phisms (resp. the Lie algebra of outer derivations) of a finite simple gro up \\(G\\) (resp. a finite-dimensional simple Lie algebra \\(L\\)). While the former is known to be true as a consequence of the classification of f inite simple groups\, the latter is false over fields of small characteris tic \\(p=2\,3\\). We will finish the talk by presenting a new family of co unterexamples to the Zassenhaus conjecture over fields of characteristic \ \(p=3\\)\, as well as commenting some advances for \\(p=2\\).\n LOCATION:https://researchseminars.org/talk/WienGAGT/30/ END:VEVENT END:VCALENDAR