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.

Decompositions in theorems in classical Fourier analysis which decompose a function into large Fourier coefficients and a part that is pseudorandom

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.

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.