Previous Conferences & Workshops

Given a smooth knot K in the 3-sphere, a classic question in knot theory is: What surfaces in the 4-ball have boundary equal to K? One can also consider immersed surfaces and ask a “geography” question: What combinations of genus and double points...

Modern deep generative models like GANs, VAEs and invertible flows are showing amazing results on modeling high-dimensional distributions, especially for images. We will show how they can be used to solve inverse problems by generalizing compressed...

Langlands’s functoriality conjectures predict the existence of “liftings” of automorphic representations along morphisms of L-groups. A basic case of interest comes from the irreducible algebraic representations of GL(2), thought of as the L-group...

In 1976 Dennis Sullivan gave an example of a smooth vector-field on a compact (Riemannian) 5-dimensional manifold in which all the orbits are closed but for which there is no upper bound to the length of a closed orbit. (At first this doesn't even...

There has been tremendous progress in designing accurate black-box prediction methods (boosting, random forests, bagging, neural nets, etc.) but for deployment in the real world, it is useful to quantify uncertainty beyond making point-predictions...

This talk aims to summarize a project I was involved in during the past 5 years, with the hope of explaining our most complete understanding so far, as well as challenges and open problems. The main messages of this project are summarized below; I...

We present a purely variational approach to the regularity theory for the Monge-Ampère equation, or rather optimal transportation, introduced with M. Goldman. Following De Giorgi’s philosophy for the regularity theory of minimal surfaces, it is...

The dichotomy between structure and randomness plays an important role in areas such as combinatorics and number theory. I will discuss a similar dichotomy in complexity theory, and illustrate it with three examples of my own work: (i) An...

There is growing interest in looking at operations on quantum cohomology that take into account symmetries in the holomorphic spheres (such as the quantum Steenrod powers, using a Z/p-symmetry). In order to prove relations between them, one needs to...

There are several broad insights we can draw from computational models of human cognition in order to build more human-like forms of machine learning. (1) The brain has a great deal of built-in structure, yet still tremendous need and potential for...