Past Events
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-…
Shtuka is a species of mathematical creature featuring multiple legs. It is born in association with the algebraic symmetry encoded by an algebraic group. The movement and transformation of its legs simultaneously realize combinatoric symmetry (encoded by Hecke action) and arithmetic symmetry (…
Approximate message passing (AMP) is a family of iterative algorithms that are known to optimally solve many high-dimensional statistics optimization problems. In this talk, I will explain how to simulate a broad class of AMP algorithms in polynomial time using “local statistics hierarchy”…
The problem of bounding moments of families of L-functions has seen great progress recently. Using techniques developed to tackle this problem, we will discuss how to give sharp upper and lower bounds on high moments of unweighted Dirichlet character sums. In particular, we will explore the…
Given a positive factorisation of the identity in the mapping class group of a surface S, we can associate to it a Lefschetz fibration over the sphere with S as a regular fiber. Its total space X is a symplectic 4-manifold, so it is a natural question to ask what kind of invariants of X can be…
The (2+1)D SOS model above a hard wall is a random surface studied in statistical mechanics, among other reasons, to approximate the interface in the 3D Ising model. I will discuss the problem of understanding scaling limits of the level lines of this surface, through the lens of Gibbsian line…
Abstract: In this talk we are going to explore “real” zeros of holomorphic Hecke cusp of large weight on the modular surface. Ghosh and Sarnak established that the number of real zeros tends to infinity as the weight $k$ goes to infinity. To do so, they studied the behavior of holomorphic…
Last time we have seen that the conformal area of a compact surface introduced by Li—Yau gives an upper bound of the first eigenvalue. In this talk, I will talk about more results on the first eigenvalue of compact surfaces, including Hersch’ result on S², Li—Yau’s result on RP²…