Announcement
More talks will be added, and the details will appear on this page once confirmed.
For the past seminar talks, please visit here.
Talk 1
Speaker: Dr Naganori Yamaguchi (山口永悟), Institute of Science Tokyo
Date & Time: 25th November (Tuesday) 13:00 -- 14:15
Venue: E6-1, Rm 1401 (최석정강의실)
Title: The anabelian geometry of arithmetic surfaces (Joint work with R. Shimizu)
Abstract: Prof. S. Mochizuki proved the Grothendieck conjecture for hyperbolic curves over sub-p-adic fields; that is, any isomorphism between such curves can be reconstructed from an isomorphism of their étale fundamental groups. In this talk we introduce the (relative, semi-absolute) Grothendieck conjecture for arithmetic surfaces. If time allows, we will also touch on counterexamples due to Y. Ihara when the Dedekind scheme has every characteristic point. This work is joint with R. Shimizu (Institute of Science Tokyo).
Talk 2
Speaker: Seung-Hyeon Hyeon (현승현), Institute of Science Tokyo
Date & Time: 25th November (Tuesday) 14:30 -- 15:45
Venue: E6-1, Rm 1401 (최석정강의실)
Title: The $m$-step solvable anabelian geometry of mixed-characteristic local fields
Abstract: Let $K_\circ$ (resp. $K_\bullet$) be a mixed-characteristic local field, and $G_{K_\circ}$ (resp. $G_{K_\bullet}$) its absolute Galois group. Mochizuki (1997) has shown that every isomorphism between $G_{K_\circ}$ and $G_{K_\bullet}$ that preserves the ramification filtration is induced by some field isomorphism between $K_\circ$ and $K_\bullet$. In particular, if there exists an isomorphism between $G_{K_\circ}$ and $G_{K_\bullet}$ that respects the ramification filtration, then there also exists a field isomorphism between $K_\circ$ and $K_\bullet$. In this talk, I would like to introduce a recent result that can be considered as an “$m$-step solvable version” of that of Mochizuki, alongside the \emph{mono-anabelian} aspect of the theory.
2nd December (Tuesday) 13:00 -- 14:00
Speaker: Dr Stefan Reppen (UC Berkeley)
Venue: E6-1, Rm 1401 (최석정강의실)
Title: Singularities in the Ekedahl-Oort stratification
Abstract: We consider the Ekedahl-Oort stratification on the special fiber of an abelian type Shimura variety at a prime of good reduction. This stratification was first defined by Oort in the Siegel case by declaring two points to lie in the same stratum if the p-torsion of the corresponding abelian varieties are isomorphic. The definition was extended to abelian type Shimura varieties in a series of papers (notably by Viehmann-Wedhorn, Zhang, Shen-Zhang) with a gradual shift from the language of p-torsion to the language of G-zips. Although much is known about the strata themselves, little is known about the geometry of their closures. In the talk I will present recent work with Lorenzo La Porta and Jean-Stefan Koskivirta giving criteria for the normality and Cohen-Macaulayness of unions of EO-strata.