# Past Events

In this talk, we explain that (infinite dimensional) Teichmueller spaces associated to hyperbolic surfaces with absolute boundary carry Hamiltonian actions of the Virasoro algebra. If time permits, we will also state some open problems for surfaces with marked points. Our study is motivated on…

The main theme of the talk is the combinatorics of lattice polygons and its relationship to the geometry of the associated toric surfaces. Our point of view is to measure the complexity of lattice polygons via the complexity of geometric objects to which they give rise. For the latter, we will…

Smyth asked in the 1980s which linear relations with integral coefficients a_1 x_1 + ... + a_r x_r could hold when x_1, ... x_r are Galois conjugates. He found a necessary condition, which he conjectured was sufficient. Surprisingly, this problem, which appears to be about algebraic…

Work of Hanselman-Rasmussen-Watson has shown that the bordered Floer invariants for a 3-manifold with torus boundary can be represented as a collection of (decorated) immersed curves in the punctured torus; moreover, the Heegaard Floer homology of the closed manifold obtained by gluing two such…

We study the branching random walk under a "hard wall constraint", namely when the heights of all particles in the most recent generation are conditioned to be positive. We obtain sharp asymptotics for the probability of this event and for various statistics, conditional on its occurrence. In…

For each compact, orientable surface whose connected components have non-empty boundary, we define a dg category that categorifies the Temperley--Lieb skein of the surface. In the case when the surface is a disk, our categories are quasi-equivalent to the so-called "Bar-Natan category": the…

Abstract: In an effort to explain how anomalous dissipation of energy occurs in hydrodynamic turbulence, Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations may fail to exhibit conservation of energy if their spatial regularity is below 1/3-Hölder. I will…

The binary perceptron problem asks us to find a sign vector in the intersection of independently chosen random halfspaces with a fixed intercept. The computational landscape of the binary perceptron is not yet well-understood. In some regimes there may be an information-computation gap, but…

Given an étale Z_p-local system of rank n on an algebraic variety X, continuous cohomology classes of the group GL_n(Z_p) give rise to classes in (absolute) étale cohomology of the variety. These characteristic classes can be thought of as p-adic analogs of Chern-Simons characteristic classes of…