School of Mathematics

Classification of Representations

Jim Arthur
University of Toronto
April 28, 2011

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

Suppose that G is a connected, quasisplit, orthogonal or symplectic group over a field F of characteristic 0. We shall describe a classification of the irreducible representations of G(F) if F is local, and the automorphic representations of G in the discrete spectrum if F is global. The classification is by harmonic analysis and endoscopic transfer, which ultimately ties the representations of G to those of general linear groups.

On the Comparison of Trace Formulas

Jim Arthur
University of Toronto
April 28, 2011

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

We shall recall the spectral terms from the trace formula for G and its stabilaization, as well as corresponding terms from the twisted trace formula for GL(N). We shall then discuss aspects of the proof of the theorems stated in the first talk that are related to the comparison of these formulas.

Serre's Conjectures on the Number of Rational Points of Bounded Height

Per Salberger
Chalmers University of Technology
April 28, 2011

JOINT IAS/PU NUMBER THEORY SEMINAR

We give a survey of recent results on conjectures of Heath-Brown and Serre on the asymptotic density of rational points of bounded height. The main tool in the proofs is a new global determinant method inspired by the local real and p-adic determinant methods of Bombieri-Pila and Heath-Brown.

Pseudorandomness in Mathematics and Computer Science Mini-Workshop

Institute for Advanced Study
April 22, 2011

In math, one often studies random aspects of deterministic systems and structures.  In CS, one often tries to efficiently create structures and systems with specific random-like properties.  Recent work has shown many connections between these two approaches through the concept of "pseudorandomness".  This workshop highlights these connections, aimed at a joint audience of mathematicians and computer scientists.

Universality in the 2D Coulomb Gas

Pierluigi Falco
Member, School of Mathematics
April 20, 2011

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.

New Tools for Graph Coloring

Rong Ge
Princeton University
April 19, 2011

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.