Past Events

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...

The Torelli group is the subgroup of the mapping class group of a surface which acts trivially on the surface's first homology group. Despite the pioneering work of Birman, Johnson, and many others numerous basic questions about it remain open. I...

For the efficient solution of large, sparse, linear systems of equations, Ax = b, we usually need a preconditioning matrix P, in an appropriate sense close to the inverse of A, such that solving PAx = Pb converges fast. If we need to solve a sequence...

I will present a global construction of the Neron model for degenerating families of intermediate Jacobians; a classical case would be families of abelian varieties. The construction is based on Saito's theory of mixed Hodge modules; a nice feature...

Traveling fronts are special solutions of reaction-diffusion equations which model phenomena such as propagation of species in an environment or spreading of flames in combustible media. In this talk we will address questions of existence, uniqueness...

How do simple local interactions combine to produce complex large-scale structure and patterns? The abelian sandpile model provides a beautiful test case. I'll discuss a pair of conjectures about the scale invariance and dimensional reduction of the...

The "colored Tverberg problem" asks for a smallest size of the color classes in a (d+1)-colored point set C in R^d that forces the existence of an intersecting family of r "rainbow" simplices with disjoint, multicolored vertex sets from C. Using...

In the early 60s Kesten showed that self-avoiding walk in the upper half plane has a decomposition into an i.i.d. sequence of "irreducible bridges". Loosely defined, a bridge is a self-avoiding path that achieves its minimum and maximum heights at...