Previous Conferences & Workshops

We will discuss some arithmetic counting problems, ranging from the antique (how many squarefree integers are there in [0 . . N]?) to the au courant (conjectures of Bhargava and Cohen-Lenstra about the distributions of discriminants and of class...

We discuss the global regularity vs. finite time breakdown in nonlinear convection driven by different models of forcing. Finite time breakdown depends on whether the initial configuration crosses intrinsic, O(1) critical thresholds (CT). Our...

A corollary of a celebrated theorem of Nash and Kuiper is the existence of $C^1$ isometric embeddings of the standard 2-sphere in arbitrarily small balls of the euclidean 3-d space. On the contrary, the image of $C^2$ isometric embeddings are all...

In this talk, I will first give an overview of recent progress on the scattering conjecture and rigidity conjecture for mass critical NLS. Then I will describe our recent results concerning both conjectures for L_2 initial data. I will also discuss...

A halfspace (a.k.a. threshold) is a boolean function h : {-1,1}^n --> {-1,1} of the form h(x) = sign(w_0 + w_1 x_1 + ... + w_n x_n), where the weights w_i are arbitrary real numbers. Halfspaces are studied extensively in the theories of complexity...

This talk is about renormalization group methods for quantum field theory and classical statistical mechanics. The renormalization group is not a group but a technique for reducing infinite dimensional integrals with strong correlations to a...

The Schroedinger (and Landau-Lifshitz) map equations are a basic model in ferromagnetism, and a natural geometric (hence nonlinear) version of the Schroedinger (and Schroedinger-heat) equation. While there has been recent progress on the question of...

We construct new solutions to the $\sigma_k$-Yamabe problem on compact manifolds by considering the connected sum of two nondegenerate solutions $(M^n_1,g_1)$ and $(M^n_2,g_2)$, for any $2 \leq 2k < n$.