Video Lectures

In this talk, I will discuss the solution to several problems in two closely related settings: set families in 2^[n] with many disjoint pairs, and low-rank matrices with many zero entries.

Highlights include a resolution of an old question of Daykin...

Locally conformally symplectic (LCS) manifolds are generalisations of symplectic manifolds where the 2-form is not closed but instead satisfies the identity dω = η ∧ ω for a closed 1-form η. The study of these manifolds is equivalent to that of...

The past few years have seen rapid development in arithmetic statistics over function fields over finite fields, questions like:  what is the distribution of the ell-primary part of the class group of a random quadratic extension of F_q(t)?  (Cohen...

Since the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary...

Direct-product testers” are used in the design of (some) probabilistically checkable proofs (PCPs), which, in turn, play a fundamental role in modern complexity theory and cryptography. We investigate the direct-product testability of certain...