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Finitely Presented Groups in Arithmetic Geometry

NUMBER THEORY

September 15, 2021      3:00 pm
Speaker: Mark Shusterman - Harvard University

We discuss the problem of determining the number of generators and relations of several profinite groups of arithmetic and geometric origin. These include etale fundamental groups of smooth projective varieties,...
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From Ramanujan to K-theory

NUMBER THEORY

April 28, 2021      3:00 pm
Speaker: Frank Calegari - University of Chicago

The Rogers-Ramanujan identity is an equality between a certain “q-series” (given as an infinite sum) and a certain modular form (given as an infinite product). Motivated by ideas from physics,...
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The absolute prismatic site

NUMBER THEORY

April 21, 2021      3:00 pm
Speaker: Bhargav Bhatt - University of Michigan

The absolute prismatic site of a p-adic formal scheme carries interesting arithmetic and geometric information attached to the formal scheme. In this talk, after recalling the definition of this site,...
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Arithmetic curves lying in compact subsets of affine schemes

NUMBER THEORY

April 14, 2021      3:00 pm
Speaker: François Charles - Université Paris-Sud

We will describe the notion of affine schemes and their modifications in the context of Arakelov geometry. Using geometry of numbers in infinite rank, we will study their cohomological properties....
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The motivic Satake equivalence

NUMBER THEORY

April 7, 2021      3:00 pm
Speaker: Timo Richarz - TU Darmstadt

The geometric Satake equivalence due to Lusztig, Drinfeld, Ginzburg, Mirković and Vilonen is an indispensable tool in the Langlands program. Versions of this equivalence are known for different cohomology theories such as...
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Single-valued Hodge, p-adic^2, and tropical integration

NUMBER THEORY

March 24, 2021      3:00 pm
Speaker: Daniel Litt - University of Georgia

I'll discuss 4 different types of integration -- one in the complex setting, one in the tropical setting, and two in the p-adic setting, and the relationships between them. In particular, we...
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Modular forms on G_2

NUMBER THEORY

March 17, 2021      3:00 pm
Speaker: Aaron Pollack - UCSD

Following work of Gross-Wallach, Gan-Gross-Savin defined what are called "modular forms" on the split exceptional group G_2.  These are a special class of automorphic forms on G_2.   I'll review their...
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Existence of CM lifts for points on Shimura varieties

NUMBER THEORY

March 10, 2021      3:00 pm
Speaker: Keerthi Madapusi Pera - Boston College

I'll explain a very simple proof of the fact that K3 surfaces of finite height admit (many) CM lifts, a result due independently to Ito-Ito-Koshikawa and Z. Yang, which was...
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