Video Lectures

Consider the p-biased distribution over 0,1n, in which each coordinate independently is sampled according to a p-biased bit. A sharp-threshold result studies the behavior of Boolean functions over the hypercube under different p-biased measures, and...

The Hamiltonian formulation of mechanics has many advantages, but its standard presentation destroys manifest covariance. This can be avoided by using the "covariant phase formalism" of Iyer and Wald, but until recently this formalism has suffered...

Why deep learning models, trained on many machine learning tasks, can obtain nearly perfect predictions of unseen data sampled from the same distribution but are extremely vulnerable to small perturbations of the input? How can adversarial training...

In this talk, I will discuss my two recent works on Energy-Based Models. In the first work, I discuss how we can reinterpret standard classification architectures as class conditional energy-based models and train them using recently proposed...

High dimensional expansion generalizes edge and spectral expansion in graphs to hypergraphs (viewed as higher dimensional simplicial complexes). It is a tool that allows analysis of PCP agreement rests, mixing of Markov chains, and construction of...

We provide geometric sufficient conditions for Reifenberg flat sets of any integer dimension in Euclidean space to be parametrized by a Lipschitz map with Hölder derivatives. The conditions use a Jones type square function and all statements are...

We will ask how many Lagrangian tori, say with an integral area class, can be `packed' into a given symplectic manifold. Similarly, given an arrangement of such tori, like the integral product tori in Euclidean space, one can ask about the...

Striving to make contact with mathematics and to be consistent with neuroanatomy at the same time, I propose an idealized picture of the cerebral cortex consisting of a hierarchical network of brain regions each further subdivided into...

Machine Learning is invaluable for extracting insights from large volumes of data. A key assumption enabling many methods, however, is having access to training data comprising independent observations from the entire distribution of relevant data...