Video Lectures

I will describe some new "coarse-graining" methods in quantitative homogenization and how they can be used to give rigorous versions of certain heuristic "renormalization group" arguments in physics, with a focus on several examples.

A fractal uncertainty principle (FUP) roughly says that a 
function and its Fourier transform cannot both be concentrated on a 
fractal set. These were introduced to harmonic analysis in order to 
prove new results in quantum chaos: if eigenfunctions...

Cohomology of classifying space/stack of a group G is the home which resides all characteristic classes of G-bundles/torsors. In this talk, we will try to explain some results on Hodge/de Rham cohomology of BG where G is a p-power order commutative...

A weighted pseudorandom generator (WPRG) is a generalization of a pseudorandom generator (PRG) in which, roughly speaking, probabilities are replaced with weights that are permitted to be positive or negative. In this talk, we present new explicit...

In the study of Hamiltonian systems, integrable dynamics play a crucial role. Integrability, however, appears to be a delicate property that is not expected to persist under generic small perturbations. Understanding the essence of this fragility...

Is randomness ever necessary for space-efficient computation? It is commonly conjectured that L = BPL, meaning that halting decision algorithms can always be derandomized without increasing their space complexity by more than a constant factor. In...

The C0 distance on the space of contact forms on a contact manifold has been studied recently by different authors. It can be thought of as an analogue for Reeb flows of the Hofer metric on the space of Hamiltonian diffeomorphisms. In this talk, I...

We used more than 25 million galaxies in the Subaru Hyper Suprime-Cam (HSC) shear catalog in the redshift range up to z~1.5 to measure weak lensing distortion effects due to large-scale structures. We used the measured weak lensing signals to...

Consider a function on Rn that can be written as a sum of functions f=f1 + f2 + ... + fm, for m greater than n.

The question of approximating f by a reweighted sum using only a small number of summands has many applications in CS theory, mathematical...