School of Mathematics

Knot Floer homology is an invariant for knots in three-space, defined as a Lagrangian Floer homology in a symmetric product. It has the form of a bigraded vector space, encoding topological information about the knot. I will discuss an algebraic...

Competitive optimization is needed for many ML problems such as training GANs, robust reinforcement learning, and adversarial learning. Standard approaches to competitive optimization involve each agent independently optimizing their objective...

Data-driven design is making headway into a number of application areas, including protein, small-molecule, and materials engineering. The design goal is to construct an object with desired properties, such as a protein that binds to a target more...

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...