More group photos

• [1], [2], [3]

All lectures take place in Room 101, Bldg 28 (28동 101호).

Speakers

• Dongryul Kim (Stanford)

• Yong Suk Moon (BIMSA)

• Gyujin Oh (Columbia)

• Koji Shimizu (Tsinghua)

• Sug Woo Shin (UC Berkeley / KIAS)

• Yihang Zhu (Tsinghua)

Schedules

• 1/12 Mon         09:50 -- 10:00     Registration

                                10:00 -- 10:50     Shimizu

                                11:10 -- 12:00     Oh

                                14:00 -- 14:50     Moon

                                15:10 -- 16:00     Kim

                                16:30 -- 17:30     Discussion

• 1/13 Tue           10:00 -- 10:50     Shimizu

                                11:10 -- 12:00     Oh

                                14:00 -- 14:50     Moon

                                15:10 -- 16:00     Kim

                                16:30 -- 17:30     Discussion

• 1/14 Wed         No lectures (Excursion or private discussion)

• 1/15 Thu           10:00 -- 10:50     Shimizu

                                11:10 -- 12:00     Oh

                                14:00 -- 14:50     Kim

                                15:10 -- 16:10     Zhu

                                16:30 -- 17:30     Shin

• 1/16 Fri             10:00 -- 10:50     Shimizu

                                11:10 -- 12:00     Oh

                                14:00 -- 14:50     Kim

                                15:20 -- 16:20     Discussion

Abstract

• Oh, Gyujin  & Shimizu, Koji

      Title: Moduli stack of isocrystals

      Abstract: On a smooth algebraic variety over the complex numbers, any local system is associated with a vector bundle with flat connection, via the Riemann--Hilbert correspondence. Isocrystals are p-adic analogues of local systems for varieties over finite fields of characteristic p, which exhibit characteristics of both local systems and differential equations. The goal of this series of talks is to explain our recent construction of the moduli stacks of isocrystals. Along the way, we will explain the motivation for this problem and the relevant background in p-adic cohomology and the theory of rigid analytic stacks.

• Kim Dongryul

      Title: Mixed characteristic shtukas on Shimura varieties

      Abstract: Taking the $p$-power torsion points of an abelian variety defines a $p$-divisible group, and a global application of this construction yields a universal $p$-divisible group over the Siegel modular variety. This ``$p$-adic realization'' of a motive can be generalized to other Shimura varieties and their integral models in many cases. We will discuss Scholze--Weinstein's theory of mixed characteristic shtukas and Pappas--Rapoport's construction of universal shtukas defined over Shimura varieties. We will also discuss how we may understand and define isogenies between points of the Shimura variety through its universal shtuka.

• Moon, Yong Suk

Title: Spectral halo conjecture and Emerton-Gee stack

Abstract: The spectral halo conjecture by Coleman-Mazur and Buzzard-Kilford concerns the geometry of the eigencurve over the boundary of weight space; it predicts the ratios between Up-slopes and p-adic valuations of weight parameter over the halo region. We will discuss a (phi, Gamma)-module theoretic approach to this conjecture, based on the geometry of Emerton-Gee stack. This is a joint work in progress with John Bergdall, Brandon Levin, and Liang Xiao.

• Shin, Sug Woo 

Title: Igusa varieties

Abstract: Igusa varieties naturally arise in the study of mod p special fibers of Shimura varieties. I will discuss old and new results on Igusa varieties with emphasis on the problem of computing their etale cohomology.

• Zhu, Yihang

Title: Towards Local Langlands-Kottwitz Method

Abstract: The Langlands–Kottwitz method aims to link the Hasse–Weil zeta functions of Shimura varieties with automorphic $L$-functions. A central component of this approach is a global trace formula that connects the cohomology of Shimura varieties to objects in local harmonic analysis—specifically orbital and twisted orbital integrals—which appear in the Arthur–Selberg trace formula. After surveying the current status of this field, we present a recently discovered local analogue of the global trace formula. This analogue relates the cohomology of certain local Shimura varieties to twisted orbital integrals. We conclude by explaining how this local perspective enhances our understanding of the global Langlands–Kottwitz program.