For a compact Lie group $G$, its massless Coulomb branch algebra is the $G$-equivariant Borel-Moore homology of its based loop space. This algebra is the same as the algebra of regular functions on the BFM space. In this talk, we will explain how this algebra acts on the equivariant symplectic cohomology of Hamiltonian $G$-manifolds when the symplectic manifolds are open and convex. This is a generalization of the closed case where symplectic cohomology is replaced with quantum cohomology. Following Teleman, we also explain how it relates to the Coulomb branch algebra of cotangent-type representations. This is joint work with Eduardo González and Dan Pomerleano.

We will present a matching upper and lower bound for the right tail probability of the maximum of a random model of the Riemann zeta function over short intervals.  In particular, we show that the right tail interpolates between that of log-correlated and IID random variables as the interval varies in length. We will also discuss a new normalization for the moments over short intervals. This result follows the recent work of Arguin-Dubach-Hartung and is inspired by a conjecture by Fyodorov-Hiary-Keating on the local maximum over short intervals.

I will discuss certain dynamics of interacting particles in interlacing arrays with inhomogeneous, in space and time, jump probabilities and their relations to conditioned random walks and random tilings of the Aztec diamond.

email Hannah Hughes for further information.