Past Events

An instance of a constraint satisfaction problem is called non-redundant if no constraint is implied by the rest; that is, for each constraint, there exists an assignment that violates that constraint while satisfying all others. The non-redundancy (NRD) of a relation R is the maximum number of…

In recent years, the combined work of Guaraco, Hutchinson, Tonegawa, and Wickramasekera has established a min-max construction of minimal hypersurfaces in closed Riemannian manifolds, based on the analysis of singular limits of sequences of solutions of the Allen—Cahn equation, a semi-linear…

We will talk about new phenomena observed when studying the first moment of cubic L-functions at any s in the critical strip. We show that there is a phase transition in the moment at s=1/3, and an interesting symmetry in the moment happens between s>1/3 and s<1/3. In particular, at s=1/2…

Unknotting number is a fundamental measure of how complicated a knot is, measuring how `far' it is from the unknot via crossing changes. It is a challenging invariant to compute; a vast array of tools have been applied to its calculation, and many conjectureshave grown up…

Abstract: Diffusion processes beyond Brownian motion have recently attracted significant interest from different communities in mathematics, the physical and biological sciences. They are described by nonlocal operators with singular non-integrable kernels, such as fractional Laplacians. The…

We adapt the construction of global Kuranishi charts to the moduli space of genus 0  SFT buildings. Using these charts, we associate a flow category with any non-degenerate contact manifold where the objects are collections of Reeb orbits and morphisms are moduli of buildings. This is joint…

Sparse random graphs are widely viewed as discrete models of chaotic physical systems. Heuristically, this suggests that eigenvectors of the adjacency operator should exhibit Gaussian statistics. We prove that a broad class of random graphs, including both random regular graphs and irregular…

In 1972, Borel proved that every holomorphic map from a product of punctured unit disks to a complex Shimura variety extends to a map from a product of disks to its Baily--Borel compactification.  Recently, Oswal--Shankar--Zhu and Patel proved the corresponding p-adic statement over…

The key ingredient in the combinatorial approach to Khovanov-Rozansky homology (which categorifies the sl_N Reshetikhin–Turaev invariant) is to make sense of the (2-)category of sl_N foams. I'll explain how this was done via categorified skew Howe duality by Queffelec and Rose.

We will explore the classification of compact flat manifolds, talk about crystallographic groups, and, of course, relate all this to the eigenfunctions of the Laplacian.