Date & Time: Thursday May 23, 2024, 13:00-17:00

• 13:00-14:00: Arno Kret (Amsterdam): On the H0 of Igusa varieties

Abstract: In this talk I would like to explain my joint work with Sug Woo Shin (arxiv:2102.10690) on the computation of the degree 0 cohomology of Igusa varieties in terms of one-dimensional automorphic representations. In particular I want to discuss the applications to the Hecke orbit conjecture and irreducibility of Igusa towers, and also discuss some ideas of the proofs. 

• 14:00-14:20: Coffee Break

• 14:20-15:20: Torsten Wedhorn (Darmstadt): Moduli of truncated local G-shtukas

Abstract: We develop a general formalism to deal with truncations of displays, prismatic Breuil-Kisin modules, or local shtukas and their moduli. The talk focuses on truncated local G-shtukas and their moduli spaces. We explain how their description yields an identification of their motive to that of the motive of the stack of G-zips implying in particular an identification for (higher) Chow groups.

This is joint work with Eva Viehmann and (in part) with Can Yaylali.

• 15:40-16:40: Ben Moonen (Nijmegen): The Coleman-Oort problem - an update

Abstract: A conjecture of Coleman says that if we fix a genus g (with g>7), there are only finitely many complex curves (smooth projective, taken up to isomorphism) of genus g for which the Jacobian is an abelian variety of CM type. Via the André-Oort conjecture (now a theorem of Tsimmerman, building upon work of many others), Coleman's conjecture can be reformulated as a problem about the non-existence of special subvarieties in the Torelli locus. In my talk, I will review this problem, and I will discuss recent progress, based on ideas that come from various directions.

Please email Wushi Goldring if you have any questions: wgoldring "at" math "dot" su "dot" se