Families of Automorphic Forms and the Trace Formula: January 26 – February 1, 2014

The Simons Symposium on Families of Automorphic Forms and the Trace Formula provided an opportunity for researchers to study families of automorphic representations of higher rank groups. During the symposium participants investigated the trace formula, plancherel equidistribution and other recent techniques from harmonic analysis and representation theory with the goal to set an agenda for the field.

Non-Archimedean & Tropical Geometry: March 31-April 6, 2013

This symposium will focus on setting a clear agenda for future developments in the related fields of tropical and nonarchimedean analytic geometry. One of the goals of the meeting will be to produce high quality expository material presenting the methods, results, and ambitions of these active research areas. Another will be to identify problems in other fields of mathematics that could be amenable to tropical and nonarchimedean analytic methods and establish new rigorous links with those neighboring fields.

New Directions in Approximation Algorithms: January 27-February 2, 2013

Many of the striking advances in theoretical computer science over the past two decades concern
approximation algorithms, which compute provably near-optimal solutions to NP-hard optimization problems.
Yet the approximability of several fundamental problems such as TSP, Graph Coloring, Graph Partitioning etc.
remains an open question. For other problems the so-called PCP Theorems and more recently, the Unique Games
Conjecture (UGC), provide a complexity-theoretic explanation for the failure to design better algorithms.

Quantum Entanglement: February 3- February 9, 2013

This meeting explored exotic quantum states of matter, with a particular focus on the role of quantum entanglement. A variety of new tools arising from both the study of quantum field theoretic techniques in condensed matter physics, and from the “holographic” duality between field theories and gravity theories coming out of string theory, make this an excellent time to try and rise to the challenge of understanding exotic quantum states.