Upcoming Events
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.
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,…
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 …
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…
We study the open KPZ equation, a prototypical one-dimensional random growth model subject to boundary conditions. Using stochastic analytic tools, we show that a suitably resampled Brownian motion describes its long-time behavior.
The Lonely Runner Conjecture, due to Wills and Cusick, asserts that if n runners with distinct constant speeds run around a unit length track, all starting at a common point, then each runner is at some moment separated by a distance of at least 1/n from every other runner.
A weaker…
Starting from first principles, I will derive (a variant of) the GRPO algorithm, one of the most widely used algorithms for post-training large language models. Then I will sketch how this algorithm is implemented at scale. Finally, I will briefly describe an important open problem known as…