Colloquia/Fall2025

UW-Madison Mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.

mathcolloquium@g-groups.wisc.edu is the mailing list. Everyone in the math department is subscribed.

The main contact is Dallas Albritton. Secondary contact is Paul Apisa.

date	speaker	title	host(s)
October 3, 2025	Hong Wang (NYU and IHES)	Restriction theory and projection theorems	Seeger, Stovall, Street
Monday, October 6, 4 pm in VV B239	Wei Zhang (Distinguished Lectures) (MIT)	Gross-Zagier formula in high dimensions, I	Yang
Tuesday, October 7, 4 pm in VV B239	Wei Zhang (Distinguished Lectures) (MIT)	Gross-Zagier formula in high dimensions, II
Wednesday, October 8, 12 pm in Birge 302	Wei Zhang (Distinguished Lectures) (MIT)	Proportionality and the arithmetic volumes of Shimura varieties and the moduli of Shtukas
October 10, 2025	Joseph Maher (CUNY)	TBD	Uyanik
October 17, 2025	Vadim Gorin (UC Berkeley)		Gurevich
Thursday, 4 pm, October 23, 2025	Aaron Naber (Distinguished Lectures) (IAS)		Waldron
October 24, 2025	Aaron Naber (Distinguished Lectures) (IAS)		Waldron
October 31, 2025	Henri Berestycki (Maryland/EHESS)		Graham
November 7, 2025
Wednesday, 4 pm, November 12, 2025	Rachel Greenfeld (Northwestern)		Seeger, Stovall
November 21, 2025	Reserved		Smith
November 28, 2025	Thanksgiving Week (No Colloquium)
December 5, 2025	Reserved		Smith

Abstracts

October 3: Hong Wang (NYU and IHES)

Title: Restriction theory and projection theorems

Abstract: Restriction theory studies functions whose Fourier transforms are supported on some curved manifold in R^n (for example, solutions to the linear Schrodinger equation or to the wave equation). Projection theorems study the Hausdorff dimension of fractal sets under orthogonal projections from R^n to its subspaces. We will survey some recent works in both fields and discuss their interactions.

October 6: Wei Zhang (MIT)

Lectures 1 and 2: Monday (Oct. 6) and Tuesday (Oct. 7) 4-5pm, VV B239

Title: Gross-Zagier formula in high dimensions (I, II)

Abstract: In their 1986 paper, Gross and Zagier proved a formula relating a special rational point on an elliptic curve to the first derivative of the L-function associated with that curve. The Gross–Zagier formula, together with Kolyvagin’s Euler system, yielded a major advance toward the Birch–Swinnerton-Dyer conjecture for elliptic curves. Since then, generalizing this fundamental result to higher-dimensional algebraic varieties has become a central area of interest. In this talk, I will present some of these generalizations, focusing on relatively recent developments, with particular emphasis on Kudla’s program and the arithmetic Gan–Gross–Prasad conjecture. Much like the Gross–Zagier formula, these generalizations have found important applications to the Beilinson–Bloch–Kato conjecture, which extends the Birch–Swinnerton-Dyer conjecture to higher-dimensional varieties.

Lecture 3: Wednesday, Oct. 8, 12-1pm. Birge B302

Title: Proportionality and the arithmetic volumes of Shimura varieties and the moduli of Shtukas

Abstract: The volume of a locally symmetric space can be expressed essentially as a product of special values of zeta functions. More generally, Hirzebruch’s proportionality theorem, later extended by Mumford, describes how to integrate any Chern class polynomial on a locally symmetric space. A natural next step is to study the arithmetic volumes of Shimura varieties, as well as their analogues for the moduli spaces of Drinfeld Shtukas over function fields. In this talk, we will report on joint work in progress with Tony Feng and Zhiwei Yun addressing this question.