Past Events
Two embedded smooth surfaces in a 4-manifold are an exotic pair if they are topologically, but not smoothly, isotopic A subtle point is that such surfaces might be still equivalent, i.e., related by a diffeomorphism. The first examples of this phenomenon are due to Baraglia (2024), using…
Mason is a flooring installer who’s just landed a huge gig: the president has tasked him with tiling his new 90000-square-foot ballroom! Upon arrival, he finds out that the room is shaped like a hexagon and he’s been given millions of rhombus tiles to put on the ground however he likes. Mason is…
Teleman conjectured that the mirror of a Hamiltonian action on a symplectic manifold is a holomorphic fibration. In this talk, I will explain this from the perspective of equivariant Lagrangian Floer theory and correspondence for symplectic quotients. Moreover, we propose a …
A k-index model is a classical statistical model describing the dependency of a response variable y onto an input vector of covariates x. It posits that y depends on x only via its projection onto a k-dimensional subspace. Learning in this model boils down to estimating this subspace from data,…
A result of Jan Nekovář says that the Galois action on p-adic intersection cohomology of Hilbert modular varieties with coefficients in automorphic local systems is semisimple. We will explain a new proof of this result for the non-CM part of the cohomology. Interestingly, Nekovář’s…
In this talk, we will introduce the Dirichlet-to-Neumann map and survey several important related results. In particular, we will we derive the spectral asymptotics for the Steklov problem on smooth Riemannian manifolds with boundary. We will then discuss a few open conjectures.
For a prime p, let {C_n} be a Z_p-tower of smooth projective curves over a finite field of characteristic p. The p-part of the class group of the function field of C_n is known to depend on n in a regular way. In characteristic p, the p-divisible group of the Jacobian of C_n is a geometric…
We present recent works with Zaher Hani and Xiao Ma, in which we derive the Boltzmann equation from the hard sphere dynamics in the Boltzmann-Grad limit, for the full time range in which the (strong) solution to the Boltzmann equation exists. This is done in the Euclidean setting in any…
Random walks on graphs can mix slowly. To speed it up, imagine that at each step instead of choosing the neighbor at random, there is a small probability eps>0 that we can choose it. We show that in this case, at least for graphs of bounded degree, there is a way to steer the walk so that we…