School of Mathematics

Implied Existence for 3-D Reeb Dynamics

Al Momin
Purdue University
November 19, 2010

Perturbation Theory for Band Matrices

Sasha Sodin
November 19, 2010

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

Endoscopic Transfer of Depth-Zero Suprcuspidal L-Packets

Tasho Kaletha
Princeton University; Member, School of Mathematics
November 18, 2010

Potential Automorphy for Compatible Systems of l-Adic Galois Representations

David Geraghty
Princeton University; Member, School of Mathematics
November 18, 2010

I will describe a joint work with Barnet-Lamb, Gee and Taylor where we establish a potential automorphy result for compatible systems of Galois representations over totally real and CM fields. This is deduced from a potential automorphy result for single l-adic Galois representations satisfying a `diagonalizability' condition at the places dividing l.

Lecture 6

Pierre Colmez
National Center for Scientific Research; Member, School of Mathematics
November 18, 2010

A New Approach to the Local Langlands Correspondence for $GL_n$ Over p-Adic Fields

Peter Scholze
University of Bonn
November 17, 2010

Configuration Spaces of Hard Discs in a Box

Matthew Kahle
November 15, 2010

The "hard discs" model of matter has been studied intensely in statistical mechanics and theoretical chemistry for decades. From computer simulations it appears that there is a solid--liquid phase transition once the relative area of the discs is about 0.71, but little seems known mathematically. Indeed, Gian-Carlo Rota suggested that if we knew the total measure of the underlying configuration space, "we would know, for example, why water boils at 100 degrees on the basis of purely atomic calculations."

Fractional Perfect Matchings in Hypergraphs

Andrzej Rucinski
Adam Mickiewicz University in Polznan, Poland; Emory University
November 15, 2010

A perfect matching in a k-uniform hypergraph H = (V, E) on n vertices
is a set of n/k disjoint edges of H, while a fractional perfect matching
in H is a function w : E → [0, 1] such that for each v ∈ V we have
e∋v w(e) = 1. Given n ≥ 3 and 3 ≤ k ≤ n, let m be the smallest
integer such that whenever the minimum vertex degree in H satisfies
δ(H) ≥ m then H contains a perfect matching, and let m∗ be defined
analogously with respect to fractional perfect matchings. Clearly, m∗ ≤
m.