Video Lectures

One of the most important events in science dates back to 1687, when Newton published the Philosophiæ Naturalis Principia Mathematica. In this masterpiece of human thought, the famous second law of motion is laid out, which concretely and...

We will discuss a version of the Green--Tao arithmetic regularity lemma and counting lemma which works in the generality of all linear forms. In this talk we will focus on the qualitative and algebraic aspects of the result.

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...

When a globular cluster or a dwarf galaxy is tidally disrupted due to its host galactic potential, the unbound stars assemble into coherent filamentary structures known as stellar streams. Given the ordered nature of their dynamical formation...

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...

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...

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...

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...

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...