School of Mathematics

Consider a point particle flying freely on the torus and elastically bouncing back from the boundary of fixed smooth convex obstacles. This is the celebrated Sinai billiard, a rare example of a deterministic dynamical system where rigorous results...

I will describe recent progress in determination of asymptotic behavior in random constraint satisfaction problems, including the independent set problem on random graphs, random regular NAE-SAT, and random SAT. The results include sharp phase...

What is the "right" topological invariant of a large point cloud XX? Prior research has focused on estimating the full persistence diagram of XX, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient statistic...

In this talk, we will discuss the Chiu-Tamarkin complex. It is a symplectic/contact invariant that comes from the microlocal sheaf theory. I will explain how to define some capacities using the Chiu-Tamarkin complex in both symplectic and contact...

In this talk we will discuss invariants of sutured Legendrians. A sutured contact manifold can be seen as either generalizing the contactisation of a Liouville domain, or as a presentation of a contact manifold with convex boundary. Using the first...

Continuation from last time.

For homogeneous affine Springer fibers (those with GmGm symmetry), we realize them as Lagrangian cycles inside ambient symplectic varieties, and make sense of microlocal sheaves supported on these affine Springer fibers. We also propose a...

In this talk, we will discuss some joint work with Alexandru Ionescu on the nonlinear inviscid damping near point vortex and monotone shear flows in a finite channel. We will put these results in the context of long time behavior of 2d Euler...

Given the current knowledge of complex representations of finite simple groups, obtaining good upper bounds for their characters values is still a difficult problem, a satisfactory solution of which would have significant implications in a number of...

Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale...