Previous Conferences & Workshops

I will give a brief introduction to spherical varieties. With a view towards understanding the geometry of the moment map, I'll talk about the local structure theorem for spherical varieties. More concretely, if X is a spherical G-variety and B a...

Classical and quantum Hamiltonian actions of reductive groups, respectively, give rise to ubiquitous families of commuting flows and of commutative rings of operators. I will explain how a construction of Ngô (from the proof of the Fundamental Lemma...

I will show an explicit construction of a binary error correcting code with relative distance $\frac{1-\epsilon}{2}$ and relative rate $\epsilon^{2+o(1)}$. This comes close to the Gilbert-Varshamov bound that shows such codes with rate $\epsilon^2$...

Linear dynamical systems (LDSs) are a class of time-series models widely used in robotics, finance, engineering, and meteorology. I will present our "spectral filtering" approach to the identification and control of discrete-time LDSs with multi...

The classical Liouville theorem claims that any positive harmonic function in $R^n$ is a constant function. Nadirashvili conjectured that any non-constant harmonic function in $R^3$ has a zero set of infinite area. The conjecture is true and we will...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality...

This talk will survey ideas surrounding a conjecture in number theory about the structure of class groups of number fields. Each number field has associated to it a finite abelian group, the class group, and as long ago as Gauss, deep questions...

We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in polylogarithmic time on quasi-polynomially many processors. The result is obtained by a derandomization of...