# Video Lectures

### Virasoro Conformal blocks in Liouville CFT

Colin Guillarmou and Rémi Rhodes

Liouville conformal field theory is a CFT with central charge c>25 and continuous spectrum, its correlation functions on Riemann surfaces with marked points can be expressed using the bootstrap method in terms of conformal blocks. We will explain...

The Brascamp-Lieb inequality is a fundamental inequality in analysis, generalizing more classical inequalities such as Holder's inequality, the Loomis-Whitney inequality, and Young's convolution inequality: it controls the size of a product of...

### Homogeneous Structures in Subset Sums and Non-averaging Sets

David Conlon

We show that for every positive integer k there are positive constants C and c such that if A is a subset of {1, 2, ..., n} of size at least C n^{1/k}, then, for some d \leq k-1, the set of subset sums of A contains a homogeneous d-dimensional...

### Recent Progress in Randomness Extraction

Randomness is a vital resource in computation, with many applications in areas such as cryptography, data-structures and algorithm design, sampling, distributed computing, etc. However generating truly random bits is expensive, and most sources in...

### On Bennequin Type Inequality for Symplectic Caps of (S3,ξstd).

Anubhav Mukherjee

In this talk I will discuss a Bennequin type inequality for symplectic caps of S3 with standard contact structure. This has interesting applications which can help us to understand the smooth topology of symplectic caps and smoothly embedded suraces...

### Existence of Quasigeodesic Anosov Flows in Hyperbolic 3-Manifolds

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...

### Two (More) Algorithms for Set Cover

Anupam Gupta

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...

### Degree Lowering Along Arithmetic Progressions

Borys Kuca

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...

### Asymptotic Total Ergodicity and Polynomial Patterns in Finite Fields

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...

### Limit Formulas for Polynomial Ergodic Averages with Commuting Transformations

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...