# Recently Added

## Universality in the 2D Coulomb Gas

The Coulomb Gas is a model of Statistical Mechanics with a special type of phase transition. In the first part of the talk I will review the expected features conjectured by physicists and the few mathematical results so far obtained. The second part will be an introductory discussion of a general technique (Renormalization Group) to approach the problem.

## Quantum Fingerprints that Keep Secrets

In a joint work with Tsuyoshi Ito we have constructed a fingerprinting scheme (i.e., hashing) that leaks significantly less than log(1/epsilon) bits about the preimage, where epsilon is the error ("collision") probability. It is easy to see that classically this is not achievable; our construction is quantum, and it gives a new example of (unconditional) qualitative advantage of quantum computers.

## New Tools for Graph Coloring

How to color $3$ colorable graphs with few colors is a problem of longstanding interest. The best polynomial-time algorithm uses $n^{0.2130}$ colors.

We explore the possibility that more levels of Lasserre Hierarchy can give improvements over previous algorithms. While the case of general graphs is still open, we can give analyse the Lasserre relaxation for two interesting families of graphs.

## A Conversation with Alex Ross

Alex Ross, music critic of the New Yorker, joins Derek Bermel, the Institute’s Artist-in-Residence, in a discussion of the challenges in writing about music for different formats, including books, magazines, newspapers, and blogs.

## The Bernstein Center of the Category of Smooth W(k)[GL_n(F)]-Modules

## Atiyah's Connectivity, Morse Theory and Solution Sets

## Graph Sparsification by Edge-Connectivity and Random Spanning Trees

A "sparsifier" of a graph is a weighted subgraph for which every cut has approximately the same value as the original graph, up to a factor of (1 +/- eps). Sparsifiers were first studied by Benczur and Karger (1996). They have wide-ranging applications, including fast network flow algorithms, fast linear system solvers, etc. Batson, Spielman and Srivastava (2009) showed that sparsifiers with O(n/eps^2) edges exist, and they can be computed in time poly(n,eps).