Video Lectures

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...

In this talk I will explain Auroux' definition of the Fukaya category of a singular hypersurface and two results about this definition, illustrated with some examples. The first result is that Auroux' category is equivalent to the Fukaya-Seidel...

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...

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...

We define a quantum product on the cohomology of a symplectic manifold relative to a Lagrangian submanifold, with coefficients in a Novikov ring. The associativity of this product is equivalent to an open version of the WDVV equations for an...

Sums of Dirichlet characters ?n?x?(n)?n?x?(n) (where ?? is a character modulo some prime rr, say) are one of the best studied objects in analytic number theory. Their size is the subject of numerous results and conjectures, such as the Pólya...