Tropical geometry and logarithmic compactifications of reductive algebraic groups

Martin Ulirsch (Goethe-Universität Frankfurt)

Fri Jun 4, 19:00-20:00 (3 weeks from now)

Abstract: In this talk I will present two approaches towards the tropicalization of a reductive algebraic group $G$, one via Mumford’s toroidal compactification, the other via de Concini and Procesi’s wonderful compacitification. The Bruhat-Tits building of G and its root system will play a crucial role in both approaches. Using these insights I will propose two corresponding logarithmic compactifications of $G$. The first approach will provide us with a new logarithmic perspective on toric (and more generally parabolic) vector bundles, the other will allow us to study the geometry of the free group character variety at infinity, thereby providing evidence for the geometric $P=W$ conjecture. Depending on the preferences of the audience I might also engage in some wild speculations concerning a yet-to-be-discovered logarithmic incarnation of Simpson’s non-abelian Hodge correspondence. Parts of this talk are based on ongoing joint work with Lorenzo Fantini and Alex Kuronya.

algebraic geometry

Audience: researchers in the topic


Stanford algebraic geometry seminar

Series comments: This seminar requires both advance registration, and a password. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880

If you have registered once, you are always registered for the seminar, and can join any future talk using the link you receive by email. If you lose the link, feel free to reregister. This might work too: stanford.zoom.us/j/95272114542

More seminar information (including slides and videos, when available): agstanford.com

Organizer: Ravi Vakil*
*contact for this listing

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