Video Lectures

Do you want to come see some toys? "Toy" here has a special sense: an object of everyday life which can be found or made in minutes, yet which, if played with imaginatively, reveals a behavior that sets mathematicians and physicists thinking for...

In this talk, we will continue, the proof of the Central Limit theorem from my last talk. We will show that that the law of "eigenregular" Gaussian polynomials is close to a Gaussian. The proof will be based on Stein's method and will be dependent...

Given an elliptic curve \(E\) over a field \(k\), its \(p\)-torsion \(E[p]\) gives a 2-dimensional representation of the Galois group \(G_k\) over \(\mathbb F_p\). The Frey-Mazur conjecture asserts that for \(k= \mathbb Q\) and \(p > 13\), \(E\) is...

Many of the major results of modern ergodic theory can be understood in terms of a sequence of finite metric measure spaces constructed from the marginal distributions of a shift-invariant process. Most simply, the growth rate of their covering...

We present the key ideas of a new proof of Landau damping for the Vlasov-Poisson equation obtained in a joint work with Bedrossian and Masmoudi. This nonlinear transport equation is a fundamental model for describing self-interacting plasmas or...

A planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1919); we find a new connection to game...

We consider a typical situation in which probability model itself has non-negligible cumulated uncertainty. A new concept of nonlinear expectation and the corresponding non-linear distributions has been systematically investigated: cumulated...