# Past Events

- Poincaré Lecture

The seemingly magical ability of a spinning top to stay upright fascinated people for many thousands of years and in many civilizations. Clay spinning tops dated to about 6,000 years ago were excavated in Iraq. And for all these millenia another similarly counterintuitive…

We will go over the construction and basic properties of the skein lasagna module of a 4-manifold. We will also discuss the effect of attaching 3-handles on skein lasagna modules.

Entire critical points of the abelian Higgs functional are known to blow down to generalized minimal submanifolds (of codimension 2). In this talk we prove an Allard type large-scale regularity result for the zero set of solutions. In the "multiplicity one" regime, we show the uniqueness of blow…

Abstract: We will discuss cancellation of the Liouville function in almost all short intervals, and the Fourier uniformity conjecture.

Given a smoothly bounded domain in three dimensions, we may consider the curl operator acting on divergence free vector fields tangent to the domain's boundary. It turns out that one only needs to impose a finite-dimensional set of additional boundary conditions to obtain a self-adjoint operator…

Abstract: The compressible Euler equation can lead to the emergence of shock discontinuities in finite time, notably observed behind supersonic planes. A very natural way to justify these singularities involves studying solutions as inviscid limits of Navier-Stokes solutions with evanescent…

Abstract: In general, the classification of finitely generated subgroups of a given group is intractable. Restricting to two-generator subgroups in a geometric setting is an exception. For example, a two-generator subgroup of a right-angled Artin group is either free or free abelian. Jaco and…

Random regular graphs form a ubiquitous model for chaotic systems. However, the spectral properties of their adjacency matrices have proven difficult to analyze because of the strong dependence between different entries. In this talk, I will describe recent work that shows that despite this, the…

We consider a class of Lagrangians living in \mathbb{C}^3 . Their Ekholm-Shende wavefunctions, living in the HOMFLY-PT skein module, will encode open Gromov-Witten invariants in all genus and arbitrarily many boundary components. We develop a skein valued cluster theory to…