Week of March 22, 2026

March 23, 2026
Geometric Analysis and Application Singularities of Curve Shortening Flow with Convex Projections Qi Sun - University of Wisconsin-Madison 3:45pm -
KT 906
Geometry, Symmetry and Physics A high-dimensional Gross–Zagier type formula over function fields Zeyu Wang - MIT 4:30pm -
KT 801
March 24, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801
Piatetski-Shapiro Memorial Lecture Volume of the moduli of Shtukas Zhiwei Yun - MIT 4:15pm -
KT 101
March 25, 2026
Colloquium Quantum Chern–Simons invariants old and new Dan Freed - Harvard 4:00pm -
KT 205
March 26, 2026
Analysis Asymptotic stability for the degree-one vortex of the 2D abelian Yang-Mills-Higgs model under equivariant perturbations Jonas Lührmann - University of Cologne 4:00pm -
KT 201
March 27, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics Growth on groups. Gal Yehuda - 4:00pm -
KT 801 or KT217

Abstracts

Week of March 22, 2026

March 23, 2026
Geometric Analysis and Application Singularities of Curve Shortening Flow with Convex Projections 3:45pm -
KT 906

Understanding singularity formation is an important topic in the study of geometric flows. Since Gage-Hamilton-Grayson’s foundational results, it has largely been unknown how singularities of curve shortening flow form in higher codimensions. In this talk, I will present my recent results that in n dim Euclidean space, any curve with a one-to-one convex projection onto some 2-plane develops a Type I singularity and becomes asymptotically circular under curve shortening flow. As a corollary, an analog of Huisken’s conjecture for curve shortening flow is confirmed, in the sense that any closed immersed curve in n dim Euclidean space can be perturbed in n+2 dim Euclidean space to a closed immersed curve which shrinks to a round point under curve shortening flow.
Geometry, Symmetry and Physics A high-dimensional Gross–Zagier type formula over function fields 4:30pm -
KT 801

The Gross–Zagier formula relates the first derivative of the L-function for PGL(2) to (arithmetic) intersection numbers on the modular curve. It plays a central role in proving known cases of the Birch–Swinnerton-Dyer conjecture. In their celebrated work, Yun and Zhang established a function-field analogue of this formula, replacing the modular curve by moduli spaces of PGL(2)-Shtukas. New phenomena arise in this setting: higher derivatives of L-functions can also be expressed in terms of intersection numbers. However, due to the lack of properness of moduli spaces of Shtukas in higher-dimensional cases, extending this formula to higher dimensions has remained open for many years.

In this talk, I will present a higher-dimensional version of the Yun–Zhang formula. The proof uses tools from Geometric Langlands theory and aspects of the relative Langlands duality proposed by Ben-Zvi, Sakellaridis, and Venkatesh. This is joint work with Shurui Liu.

 
March 24, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
Piatetski-Shapiro Memorial Lecture Volume of the moduli of Shtukas 4:15pm -
KT 101
The volume of a locally symmetric space is essentially a product of special values of zeta functions. Its connection with automorphic forms featured in early work of Piatetski-Shapiro. There is a natural function field analog of the volume given by counting principal bundles on an algebraic curve over a finite field. 
 
Continuing in the function field setting, but going further in the arithmetic direction, we consider the volume of the moduli space of Shtukas (function field analog of Shimura varieties). I will explain how to make sense of the apparently divergent volume, and express the result in terms of higher derivatives of a curious variant of zeta functions. This is joint work with Tony Feng and Wei Zhang. 
 
March 25, 2026
Colloquium Quantum Chern–Simons invariants old and new 4:00pm -
KT 205

In the 1980s new invariants of links and 3-manifolds were put forward by Jones, Reshetikhin–Turaev, and others.  Witten’s approach was based on quantum field theory, and it spurred decades of developments in the mathematics of topological field theory.  Building on that foundation, Claudia Scheimbauer, Constantin Teleman, and I recently used the cobordism hypothesis to construct the relevant 3-dimensional topological field theories (arXiv:2601.05518).  I will review these developments and discuss the new work.
March 26, 2026
Analysis Asymptotic stability for the degree-one vortex of the 2D abelian Yang-Mills-Higgs model under equivariant perturbations 4:00pm -
KT 201

The (1+2)-dimensional abelian Yang-Mills-Higgs model is a classical relativistic field theory that features topological soliton solutions called vortices. We discuss a proof of the asymptotic stability for the degree-one vortex under equivariant perturbations in the so-called self-dual case.

This is joint work in preparation with J. Palacios, F. Pusateri, W. Schlag, and S. Shahshahani
March 27, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics Growth on groups. 4:00pm -
KT 801 or KT217

TBA