Past Events
Following Chapter 6 of Levitin–Mangoubi–Polterovich, we will discuss the heat kernel and the asymptotics of its trace. We will leverage this theory to prove Weyl's law on a Riemannian manifold, albeit with a less-than-optimal remainder estimate. Time permitting, we will discuss isospectral…
Any construction of a quantum computer would require finding good sets of quantum logic gates: finite sets of 2^n-by-2^n unitary matrices that efficiently and computably approximate arbitrary unitary matrices through short products. We explain a connection between constructing these gate…
Classical Morse homology recovers the ordinary homology of a closed manifold using the data of critical points and gradient flows. In the 1990s, Cohen-Jones-Segal proposed a categorification of this data, called the "flow category", with an eye towards developing homotopical refinements of…
We explore how contractible pieces inside 4-manifolds can magically change smooth structures when removed and reglued. Starting from the Mazur cork, we take a tour through our 4-manifold zoo and meet some interesting exotic pairs that differ only by a cork twist. There may also be infinite…
A classical theme in Riemannian geometry is that positive curvature imposes topological constraints on manifolds. In this talk, we investigate curvature conditions that distinguish Euclidean space among open contractible manifolds and the disk among compact contractible manifolds with boundary.…
[BO, 7.1-7.11] and Theorem 1.3 of F-isocrystals and de Rham cohomology. I (Berthelot-Ogus, Inventiones).
Harnack’s Curve Theorem is a classical result in plane curve geometry concerning the maximum number of connected components of a real algebraic curve. In this talk, we translate this classical problem into topology and present a proof using Smith theory and equivariant Bredon cohomology. If time…
I will describe some potential (but thus far largely unsuccessful) applications of ML techniques to proof discovery in geometric analysis.