Speaker: Dmitry Timashev is professor at Lomonosov Moscow State University. His research interests include: algebraic groups, Lie algebras, invariant theory, representation theory, equivariant algebraic geometry, spherical varieties.

Date: December 2, 2025

Time: 15:20-16: 20 pm

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Let X = G/H be a spherical homogeneous variety for a complex reductive algebraic group G. We consider the action of a maximal compact subgroup K < G on X and study the orbit space X/K. We prove that X/K is homeomorphic to a certain rational polytope P with some faces removed. This proves a conjecture of Victor Batyrev (2016) that X/K is homeomorphic to the so–called valuation cone V of X. We also describe the stratification of X/K by orbit types, namely prove that the relative interior of each face of P lies in a single stratum and find the respective K–orbit type. This result is related to a stronger version of Batyrev’s conjecture about the correspondence between the orbit type stratification of X/K and the face stratification of V.

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