Video Lectures

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...

Deep neural networks have recently seen an impressive comeback with applications both in the public sector and the sciences. However, despite their outstanding success, a comprehensive theoretical foundation of deep neural networks is still missing...

An introduction to Boolean Function Analysis We will discuss some of the basic principles and results in the study of Boolean-valued functions over the discrete hypercube using discrete Fourier analysis. In particular, we will talk about basic...

In this talk I will discuss the Sunflower Lemma and similar lemmas that prove (in various contexts) that a set/distribution can be partitioned into a structured part and a "random-looking" part. I will introduce communication complexity as a key...

Strong Average-Case Circuit Lower Bounds from Non-trivial Derandomization We prove that, unconditionally, for all constants a, NQP = NTIME[n^polylog(n)] cannot be (1/2 + 2^(-log^a n) )-approximated by 2^(log^a n)-size ACC^0 circuits. Previously, it...

This talk considers the preference modeling problem and addresses the fact that pairwise comparison data often reflects irrational choice, e.g. intransitivity. Our key observation is that two items compared in isolation from other items may be...