Past Events

In joint work with Adam Clay, we establish a necessary condition that an automorphism of an orderable group can preserve an ordering: at least one of its eigenvalues, suitably defined, must be real and positive. Applications will be given to knot...

In my work with Miguel Mendez, we provided a new combinatorial model for the coefficients appearing in the normal ordering of q-Boson words, by introducing combinatorial structures called bugs, colonies and settlements. In this lecture I will show...

The classical Sobolev inequalities are important tools for partial differential equations, probability theory and geometric analysis. In this talk, I give an introduction to the area of the Sobolev inequalities. I will then discuss some new...

In this talk, we first discuss the second iteration argument introduced by Bourgain to establish LWP of KdV with measures as initial data. Then, we establish LWP of the stochastic KdV (SKdV) with additive space-time white noise by estimating the...

While univariate polynomial interpolation has been a basic tool of scientific computing for hundreds of years, multivariate polynomial interpolation is much less understood. Already the question from which polynomial space to choose an interpolant to...

We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a...

In 1953, K. Roth proved that any subset of positive integers of positive density contains infinitely many non-trivial three-term arithmetic progressions. (By a non-trivial arithmetic progression we mean one of the form (a, a+d, a+2d) with d > 0.)...

In this talk, we first discuss the second iteration argument introduced by Bourgain to establish LWP of KdV with measures as initial data. Then, we establish LWP of the stochastic KdV (SKdV) with additive space-time white noise by estimating the...

In this talk, we discuss how probabilistic ideas are applied to study PDEs. First, we briefly go over the basic theory of Gaussian Hilbert spaces and abstract Wiener spaces to determine function spaces which capture the regularity of the Brownian...

In invasion percolation, the edges of a graph are assigned i.i.d. edge weights, and an infinite cluster is grown by recursively adding the boundary edge of minimal weight. By considering the edges whose weight is larger than all subsequently accepted...