Past Events

Kronheimer and Mrowka used gauge theory to define a functor J-sharp from a category of webs in R^3 to the category of finite-dimensional vector spaces over the field of two elements.  They also suggested a possible combinatorial replacement J-flat for J-sharp, which Khovanov and Robert…

Distinct Hamiltonian isotopy classes of Lagrangian tori in $\mathbb{CP}^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball (the affine part of $\mathbb{CP}^2$). We investigate…

In KPZ universality, an important family of models arises from 2D last-passage percolation (LPP): in a 2D i.i.d. random field, one considers the geodesic connecting two vertices, which is defined as the up-right path maximizing its weight, i.e., the sum/integral of the random field along it. A…

Abstract: In his seminal 2001 paper, Biran introduced the concept of Lagrangian Barriers, a symplectic rigidity phenomenon coming from obligatory intersections with Lagrangian submanifolds which don't come from mere topology.

In this joint work with Richard Hind and Yaron Ostrover, we…

The successive minima of an order in a degree n number field are n real numbers encoding information about the Euclidean structure of the order. How many orders in degree n number fields are there with almost prescribed successive minima, fixed Galois group, and bounded discriminant? 

I'll introduce trace formulas, with the Poisson summation formula as a model case and a trace formula for S^2 as a slightly more involved example. Time permitting, I'll also start developing some of the theory we'll need for the hyperbolic plane.

Abstract: The "area" functional takes a submanifold of a Riemannian manifold and returns its area. A natural idea is to try to use Morse theory to find critical points of the area functional (of considerable interest to geometers, these are called minimal submanifolds). I will describe what we…

Abstract: I will continue on from last week's talk, where we discussed the paper "Wilson loop expectations in lattice gauge theories with finite gauge groups" (Sky Cao, Comm. Math. Phys., 2020). In particular, I will review the definitions from last week, derive the discrete Stokes' theorem, and…

Consider the following two-player game played on the edges of the complete graph with n vertices: In each round the first player chooses b edges, which they have not previously chosen, and the second player immediately and irrevocably picks one of them and adds it to the initially empty graph G…

In their seminal work on the minimal surface system, Lawsonand Osserman conjectured that Lipschitz graphs that are critical pointsof the area functional with respect to outer variations are alsocritical with respect to domain variations. We will discuss the proof ofthis conjecture for two-…