Video Lectures

A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of the alternating group An be?

In the talk we will completely solve the problem by...

Approximate lattices in locally compact groups are approximate subgroups that are discrete and have finite co-volume. They provide natural examples of objects at the intersection of algebraic groups, ergodic theory and additive combinatorics... with...

Work of Mark Shusterman and myself has proven an analogue of Chowla's conjecture for polynomial rings over finite fields, which controls k-points correlations of the Möbius function for k bounded by a certain function of the finite field size...

Persistence modules and barcodes are used in symplectic topology to define new invariants of Hamiltonian diffeomorphisms, however methods that explicitly calculate these barcodes are often unclear. In this talk I will define one such invariant...

The ellipsoidal embedding function of a symplectic four manifold M measures how much the symplectic form on M must be dilated in order for it to admit an embedded ellipsoid of some eccentricity. It generalizes the Gromov width and ball packing...

The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is finite or not. During this short talk, I will give a sketch of the proof that, in the case of Liouville domains, the...

In this talk, I will discuss a proof of a quantitative version of the inverse theorem for Gowers uniformity norms 𝖴5 and 𝖴6 in 𝔽n2. The proof starts from an earlier partial result of Gowers and myself which reduces the inverse problem to a study of...

A theorem by Kazhdan and Ziegler says that any property of homogeneous polynomials---of a fixed degree but in an arbitrary number of variables---that is preserved under linear maps is either satisfied by all polynomials or else implies a uniform...

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of SL_3-representations. Webs and...

Ellenberg and Gijswijt drastically improved the best known upper asymptotic bound for the cardinality of a cap set in 2016. Tao introduced the notion of slice rank for tensors and showed that the Ellenberg-Gijswijt proof can be nicely formulated...