Video Lectures

I will talk about three interesting ingredients that goes into the results on H\"{o}rmander type operators I presented at Princeton (joint with Shaoming Guo and Hong Wang). They are all related to algebraic or geometric properties of multivariate...

The ruled hypersurfaces are distinguished by being comprised of lines. When this characteristic exists as a consequence of vanishing principal curvatures, it yields possibilities for comparison with cylinders extending over lower-dimensional...

A conjecture of Erdős states that for every large enough prime q, every reduced residue class modulo q is the product of two primes less than q. I will discuss my on-going work with Kaisa Matomäki establishing among other things a ternary variant of...

The online list labeling problem is a basic primitive in data structures. The goal is to store a dynamically-changing set of n items in an array of m slots, while keeping the elements in sorted order. To do so, some items may need to be moved over...

Let E be an elliptic curve defined over \Q.  The \Q¯-points of E form an abelian group on which the Galois group G\Q=\Gal(\Q¯/\Q) acts.  The usual Galois representation associated to E captures the action of G\Q on the points of finite order. ...

The classic algorithm AdaBoost allows to convert a weak learner, that is an algorithm that produces a hypothesis which is slightly better than chance, into a strong learner, achieving arbitrarily high accuracy when given enough training data. We...

Diophantine approximation deals with quantitative and qualitative aspects of approximating numbers by rationals. A major breakthrough by Kleinbock and Margulis in 1998 was to study Diophantine approximations for manifolds using homogeneous dynamics...

Conformal blocks are objects of fundamental importance in the bootstrap approach for exact solvability of 2D conformal field theory (CFT).  In this talk, we will present novel probabilistic expressions for them using the Gaussian free field in lieu...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

The recently-discoverd Hypergraph Container Method (Saxton and Thomason, Balogh, Morris and Samotij), generalizing an earlier version for graphs (Kleitman and Winston), is used extensively in recent years in extremal and probabilistic combinatroics...