Past Events

A central problem in differential geometry is understanding how the geometry of a boundary determines the geometry of its interior. Gromov's fill-in problem suggests that when a closed Riemannian manifold is filled with a region of large curvature, the extrinsic curvature of the boundary must be…

We construct the abelian category of presheaves with transfer [MWV, Chapter 1–2].

Subspace-based signal processing techniques, such as the Estimation of Signal Parameters via Rotational Invariant Techniques (ESPRIT) algorithm, are popular methods for spectral estimation. These algorithms can achieve the so-called super-resolution scaling under low noise conditions, surpassing…

I will present a result obtain in collaboration with Hitoshi Ishii and Ariela Briani, that studies the asymptotic behaviors of solutions of fully nonlinear equations in thin domains with oblique boundary conditions with a test function approach à la  Evans. The limit equation…

Abstract: Given any smooth 4-manifold bounding a Seifert manifold, the Seifert action on its boundary can be used to define their boundary Dehn twists. If the given 4-manifold is simply-connected, this Dehn twist is always topologically isotopic to the identity, but usually not smoothly isotopic…

Just as Heegaard-Floer (HF) theory is about Fukaya categories for symmetric product of Riemann surfaces, HF theory with coefficient is about  Fukaya categories of horizontal Hilbert scheme (possibly with fiberwise superpotential). This is used to give a symplectic realization of…

The Coulomb gas is a statistical physics model consisting of N particles interacting with electrostatic repulsion and with a global confining potential. I will show how a certain subharmonic structure associated with the k-point function arises. This structure implies new bounds on quantities…

I will outline the proof of the (unramified, global) geometric Langlands conjecture, emphasizing the main intermediate results used along the way. The overall project is joint with Gaitsgory, Arinkin, Beraldo, Campbell, Chen, Faergeman, Lin, and Rozenblyum. I will also describe recent work on…

We will hold an organizing session to determine which topic(s) we are gonna cover this quarter and who is gonna talk.

Operator learning has undergone rapid development in recent years and gradually emerged as a transformative machine-learning paradigm. In this talk, I will provide an overview of the operator-learning framework and explore its applications to computational problems, with a particular focus on…