# Video Lectures

A quasigeodesic in a manifold is a curve so that when lifted to the universal cover is uniformly efficient up to a bounded multiplicative and added error in measuring length. A flow is quasigeodesic if all flow lines are quasigeodesics. We prove...

In the minimum cost set cover problem, a set system is given as input, and the goal is to find a collection of sets with minimum cost whose union covers the universe. This NP-hard problem has long been known to admit logarithmic approximations...

Ever since Furstenberg proved his multiple recurrence theorem, the limiting behaviour of multiple ergodic averages along various sequences has been an important area of investigation in ergodic theory. In this talk, I will discuss averages along...

A version of the polynomial Szemer´edi theorem was shown to hold in finite fields in [BLM05]. In particular, one has patterns ${x, x + P1(n), . . . , x + Pk(n)}$ (1) for polynomials with zero constant term in large subsets of finite fields. When the...

The works of Furstenberg and Bergelson-Leibman on the Szemeredi theorem and its polynomial extension motivated the study of the limiting behavior of multiple ergodic averages of commuting transformations with polynomial iterates. Following important...

### Surfaces of Section, Anosov Reeb Flows, and the C2-Stability Conjecture for Geodesic Flows

In this talk, based on joint work with Gonzalo Contreras, I will briefly sketch the proof of the existence of global surfaces of section for the Reeb flows of closed 3-manifolds satisfying a condition à la Kupka-Smale: non-degeneracy of the closed...

I will present results establishing cancellation in short sums of arithmetic functions (in particular the von Mangoldt and divisor functions) twisted by polynomial exponential phases, or more general nilsequence phases. These results imply the...

We will discuss multilinear variants of Weyl's inequality for the exponential sums arising in pointwise convergence problems related to the Furstenberg-Bergelson-Leibman conjecture. We will also illustrate how to use the multilinear Weyl inequality...

Astrophysical black holes are surrounded by accretion disks, jets, and coronae consisting of magnetized, (near)-collisionless relativistic plasma. They produce observable high-energy radiation and it is currently unclear where and how this emission...

In this talk we present a natural generalization of a sumset conjecture of Erdos to higher orders, asserting that every subset of the integers with positive density contains a sumset $B_1+\ldots +B_k$ where $B_1, \ldots , B_k$ are infinite. Our...