Human-Made Climate Change: A Moral, Political, and Legal Issue

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.

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.

Honest Doubt

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."

Planar Convexity, Infinite Perfect Graphs and Lipschitz Continuity

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.

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.