School of Mathematics

We will investigate the geometry of the p-adic eigencurve at classical points where the Galois representation is locally trivial at p, and will give applications to Iwasawa and Hida theories.

Distributed learning protocols are designed to train on distributed data without gathering it all on a single centralized machine, thus contributing to the efficiency of the system and enhancing its privacy. We study a central problem in distributed learning, called Distributed Learning of Halfspaces: let U \subset R^d be a known domain of size n and let h:R^d —> R be an unknown target affine function. A set of examples {(u,b)} is distributed between several parties, where u \in U is a point and b = sign(h(u)) \in {-1, +1} is its label.

Existing generative models are typically based on explicit representations of probability distributions (e.g., autoregressive or VAEs) or implicit sampling procedures (e.g., GANs). We propose an alternative approach based on modeling directly the vector field of gradients of the data distribution (scores). Our framework allows flexible energy-based model architectures, requires no sampling during training or the use of adversarial training methods.

In this talk, I will address a geometric inverse problem from contact geometry: is it possible to recognize whether all orbits of a given Reeb flow are closed from the knowledge of the action spectrum? Borrowing the terminology from Riemannian geometry, Reeb flows all of whose orbits are closed are sometimes called Besse, and Besse Reeb flows all of whose orbits have the same minimal period are sometimes called Zoll.