BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Martin Ulirsch (Goethe-Universität Frankfurt) DTSTART:20210604T190000Z DTEND:20210604T200000Z DTSTAMP:20260407T214913Z UID:agstanford/51 DESCRIPTION:Title: Tropical geometry and logarithmic compactifications of reductive algeb raic groups\nby Martin Ulirsch (Goethe-Universität Frankfurt) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this talk I will present two approaches towards the tropicalization of a reductive algebra ic group $G$\, one via Mumford’s toroidal compactification\, the other v ia de Concini and Procesi’s wonderful compacitification. The Bruhat-Tits building of G and its root system will play a crucial role in both approa ches. Using these insights I will propose two corresponding logarithmic co mpactifications of $G$. The first approach will provide us with a new loga rithmic perspective on toric (and more generally parabolic) vector bundles \, the other will allow us to study the geometry of the free group charact er variety at infinity\, thereby providing evidence for the geometric $P=W $ conjecture. Depending on the preferences of the audience I might also en gage in some wild speculations concerning a yet-to-be-discovered logarithm ic incarnation of Simpson’s non-abelian Hodge correspondence. Parts of t his talk are based on ongoing joint work with Lorenzo Fantini and Alex Kur onya.\n\nThe synchronous discussion for Martin Ulirsch’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-06-04-mu (and wi ll be deleted after ~3-7 days).\n LOCATION:https://researchseminars.org/talk/agstanford/51/ END:VEVENT END:VCALENDAR