Dates: May 27 - May 30 2025
Schedule of morning talks (in Evans 939):
Tuesday - Thursday
10:15 - 11:15AM - Arpon Raksit
11:30 - 12:30PM - Matteo Tamiozzo and Mingjia Zhang
Friday May 30
10:00 - 11:00AM - Matteo Tamiozzo and Mingjia Zhang
11:30 - 12:30PM - Working group presentations
Schedule of afternoon working sessions:
Tuesday - Thursday
Raksit - 2:00 - 5:00PM in Evans 762
Tamiozzo and Zhang - 2:00 - 5:00PM in Evans 730
Topics:
Arpon Raksit - Stable homotopy theory and the cohomology of varieties
Abstract: The cohomology of varieties is a subject with many facets and interesting ties with geometric and number-theoretic matters. It also has a rich connection to stable homotopy theory, illustrated for example in the work of Thomason relating étale cohomology and algebraic K-theory, and more recently in the work of Bhatt–Morrow–Scholze on prismatic cohomology and its relation to topological Hochschild homology. In these lectures, I'll discuss some aspects of this connection, with an emphasis on developments inspired by the aforementioned work of Bhatt–Morrow Scholze. The accompanying projects will be aimed at exploring these topics and their background in more detail.
Matteo Tamiozzo and Mingjia Zhang - Igusa stacks and cohomology of Shimura varieties
Abstract: The aim of the lecture series is to illustrate how Igusa stacks can be used to study (intersection) cohomology of Shimura varieties, proving vanishing statements and Eichler–Shimura relations. We will focus throughout on the example of Siegel modular threefolds, i.e., moduli spaces of principally polarized abelian surfaces. We will first describe the geometry of the minimal compactification of Siegel modular threefolds, and the Newton stratification on their special fiber. Then we will introduce Igusa stacks and their minimal compactification. After that, we will prove t-exactness of Hecke operators acting on (suitable subcategories of) étale sheaves on Bun_G, and finally deduce the above mentioned properties of (intersection) cohomology of Igusa stacks and Siegel modular threefolds. This is based on the joint work in progress of one of us (MZ) with Ana Caraiani and Linus Hamann.