Past Events

Abstract Tropicalization is a technique that transforms algebraic geometric objects to combinatorial objects. Specifically, it associates polyhedral complex to subvarieties of an algebraic torus. One may ask which polyhedral complexes arise in this...

TBA

A fundamental problem in the area of quantum chaos is to understand the distribution of high eigenvalue eigenfunctions of the Laplacian on certain Riemannian manifolds. A particular case which is of interest to number theorists concerns hyperbolic...

The Vlasov-Poisson System models a collisionless plasma when the particle velocities are sufficiently small compared to the speed of light. It was shown in the early 90s that smooth compactly supported initial data lead to solutions that remain...

We introduce and explore some concepts of weak solution for particular nonlinear partial differential equations.These notions have their roots in the fundamental work of A. D. Aleksandrov on the Monge-Ampere measure. We also consider applications to...

In the 1990's, Greg Arone gave a description of the Snaith splitting of spaces of the form $\Omega^m \Sigma^m X$. His method extended to give a kind of functorial filtration of any space of the form Maps(K, X) where K is a finite complex. In good...

In this talk we will present our recent work on ‘’Closed geodesics in Alexandrov spaces of curvature bounded from above’’. This is an extension of Colding and Minicozzi’s width-sweepout construction of closed geodesics on closed Riemannian manifold...

Let $a,b,c \geq 2$ be integers satisfying $1/a + 1/b + 1/c > 1$. Darmon and Granville proved that the generalized Fermat equation $x^a + y^b = z^c$ has only finitely many coprime integer solutions; conjecturally something stronger is true: for $a,b,c...

Let T be the return time to the origin of a simple random walk on an infinite recurrent graph. We show that T is heavy tailed and non-concentrated. More precisely, we have i) P(T>t) > c/sqrt(t) ii) P(T=t|T>=t) C log(t)/t Inequality i) is attained...

The omega transformation takes a Schur function indexed by a partition to the Schur function indexed by the partition's transpose. In this joint work with Jeff Remmel, we explore a refinement of the omega transformation defined on the quasisymmetric...