## Perturbation Theory for Band Matrices

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

Sasha Sodin

Institute for Advanced Study

November 19, 2010

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

Al Momin

Purdue University

November 19, 2010

James E. Hansen

Columbia University

November 19, 2010

Observations of ongoing climate change, paleoclimate data, and climate simulations concur: human-made greenhouse gases have set Earth on a path to climate change with potentially dangerous consequences for humanity. James Hansen, climatologist and Adjunct Professor in the Department of Earth and Environmental Sciences at Columbia University, explains the urgency of the situation and discusses why he believes it is a moral issue that pits the rich and powerful against the young and unborn, against the defenseless, and against nature. He explores available options to avoid morally unacceptable consequences.

Pierre Colmez

National Center for Scientific Research; Member, School of Mathematics

November 18, 2010

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.

Tasho Kaletha

Princeton University; Member, School of Mathematics

November 18, 2010

Peter Scholze

University of Bonn

November 17, 2010

Paul Hodgson

Institute for Advanced Study

November 17, 2010

Artist Paul Hodgson was a Director's Visitor at the Institute in 2010. In a Friends Forum, he discussed the "difficulties in making a judgement and dubtfulness in choosing one thing over another," that underlie his current practice and emerge "both in the way that I fabricate the work, and the images that I choose to present."

Menachem Kojman

Ben Gurion University of the Negev; Member, School of Mathematics

November 16, 2010

Infinite continuous graphs emerge naturally in the geometric analysis of closed planar sets which cannot be presented as countable union of convex sets. The classification of such graphs leads in turn to properties of large classes of real functions - e.g. the class of Lipschitz continuous functions - and to meta-mathematical properties of sub-ideals of the meager ideal (the sigma-ideal generated by nowhere dense sets over a Polish space) which reduce to finite Ramsey-type relations between random graphs and perfect graphs.

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.