School of Mathematics

A classic result, due to McDuff and Schlenk, asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a remarkable structure: the function has infinitely many corners...

An important problem today is how to allow multiple distributed entities to train a shared neural network on their private data while protecting data privacy. Federated learning is a standard framework for distributed deep learning Federated...

In the last couple of years, a lot of progress has been made to enhance robustness of models against adversarial attacks. However, two major shortcomings still remain: (i) practical defenses are often vulnerable against strong “adaptive” attack...

In this talk I will discuss two lines of work involving learning in the presence of biased data and strategic behavior. In the first, we ask whether fairness constraints on learning algorithms can actually improve the accuracy of the classifier...

Some believe that truly effective and efficient reinforcement learning algorithms must explicitly construct and explicitly reason with models that capture the causal structure of the world. In short, model-based reinforcement learning is not...

Let A be an abelian variety over a number field E⊂ℂ and let v be a place of good reduction lying over a prime p. For a prime ℓ≠p, a result of Deligne implies that upon replacing E by a finite extension, the Galois representation on the ℓ-adic Tate...

Let f be a polynomial over the complex numbers with an isolated singular point at the origin and let d be a positive integer. To such a polynomial we can assign a variety called the dth contact locus of f. Morally, this corresponds to the space of d...

Fekete (1923) discovered the notion of transfinite diameter while studying the possible configurations of Galois orbits of algebraic integers in the complex plane. Based purely on the fact that the discriminants of monic integer irreducible...

Langevin diffusions are continuous-time stochastic processes that are based on the gradient of a potential function. As such they have many connections---some known and many still to be explored---to gradient-based machine learning. I'll discuss...

The IAS Number Theory group has started a new online seminar via Zoom to have more interactions among members during the Stay-at-Home Order. The seminar is modeled after the Basic Notions seminar at Harvard and is intended to be a one-hour-long Math...