Title: Structure of clusters near percolation threshold for October 20

2D continuum percolation

Speaker: Madeleine Sirugue, University of Marseille

Title: Geometric evolution equations for hypersurfaces October 20

Speaker: Gerhard Huisken, Eberhard-Karls-Universität Tübingen & Princeton University

Title: Godel, Undecidability and All That October 20

Speaker: John Conway, Princeton University

Title: Estimates of KS-entropy for hard spheres October 21

Speaker: J.R. Dorfman, University of Maryland

Presenter: Yakov Eliashberg, Princeton University October 21

Title: Topological gravity in dimensions two and four, or, Who ordered the metric? October 21

Speaker: Jack Morava, John Hopkins University

Abstract: Segal’s formulation of conformal field theory in terms of a category with Riemann surfaces as morphisms extends naturally to include what physicists call two-dimensional gravity. This in turn has a very natural generalization to four dimensions, , and both of these generalizations have deep connection with homotopy theory [cf. E.g. recent work of Tillmann and Madsen]. I’ll try to keep things relatively nontechnical, and will sketch a couple of toy model examples. This point of view suggests why Riemnannian geometry is so important in physics.

Title: Quasiconformal Mappings on Nilpotent Lie Groups October 22

Speaker: Michael Cowling, University of New South Wales

Title: The geometry of the first non-sero Steklov eigenvalue October 22

Speaker: Jose Escobar, Cornell University

Speaker: Ranee Brylinski (Pennsylvania State University) October 22

Speaker: Eleny-Nicoletta Ionel (University of Wisconsin at Madison)

Title: Smoothing properties of Schrodinger semigroups October 25

Presenter: Archil Gulisashvili, Ohio University

Abstract: The Schrodinger semigroup solves the heat equation with a potential. We consider the Kato class potentials in $R^n$ and study how the Sobolev smoothness of the solution of the corresponding heat equation depends on the smoothness of the potential.

Title: Graph Decompositions

Speaker: Paul Seymour, Mathematics Department & PACM, Princeton University *Lunch to be provided.

Topic: Rationally connected varieties over local fields October 26

Presenter: Janos Kollar, Princeton University

Abstract: One knows there is a close analogy between the ring Z of integral numbers and algebraic curves X defined over a finite field. Langlands has conjectured that either over Z or over X some kinds of harmonic analysis objects (automorphic representations of GL(r) ) and some kind of algebraic objects (l-adic representations of rank r of the Galois group) should correspond to each other. This is proved over algebraic curves X, generalizing Drinfeld's proof for the case of rank r=2. One combines Grothendieck's l-adic cohomology and fixed points formula, the geometry of Drinfeld shtukas and the Arthur-Selberg trace formula.

Title: The Infinite Numbers of Georg Cantor October 27

Speaker: John Conway, Princeton University

Title: Mass aggregation in a sticky gas October 28

Speaker: Jaroslaw Piasecki, University of Warsaw

Presenter: Yakov Eliashberg, Princeton University October 28

Title: Nonlinear vibrating strings and number theory October 28 Hill Ctr.,Rm.705

Speaker: Jean Mawhin, Université de Louvain

Speaker: Damiano Foschi, Princeton University Hill Ctr.,Rm.705

Title: TBA October 28

Speaker: Dr. Daniel Christensen, Institute for Advanced Study

Topic: TBA October 29

Presenter: Matthew Kerr, Princeton University

Topic: A degree for the contact mapping class group October 29

Presenter: Charles Epstein, Uninversity of Pennsylvania

Title: Numerical Determination of Chaotic Transfers; or, Orbit Design November 2

for Cheap Spaceflight

Speaker: Edward Belbruno, PACM & IOD

Title: TBA November 3

Speaker: John Conway, Princeton University

Presenter: Yakov Eliashberg, Princeton University November 4

Topic: TBA November 9

Presenter: A. Givental, UC Berkley

Topic: Ample divisors on holomorphic symplectic fourfolds November 9

Presenter: Brendan Hassett, University of Chicago

Abstract: Let S be a polarized K3 surface. The Picard group Pic(S) may be regarded as an integral quadratic form with respect to

the intersection pairing. There is a dictionary between the geometry of S and the arithmetic properties of this form. For example, there are criteria for the existence of smooth rational curves in terms of the integers represented by the form. This yields a simple arithmetic description of the ample cone of S. Our goal is to extend this dictionary to certain higher dimensional analogs to K3 surfaces, known as holomorphic symplectic manifolds. These include punctual Hilbert schemes (i.e., desingularized symmetric products) of K3 surfaces. We give a conjectural framework generalizing the picture for K3 surfaces and provide evidence for our conjectures.

Title: Implementation and Application of Machine-checked Proofs

Presenter: Andrew Appel, Princeton Univiversity Department of Computer Science

Topic: TBA November 10

Presenter: Giovanni Gallovotti, University of Rome

Title: Correlation kernels arising in asymptotic representation theory November 11

Speaker: Grigori Olshanskii, IITP (Moscow) and University of Pennsylvania

Abstract: Representation theory of "big" groups (like the infinite symmetric group) provides new interesting examples of random point processes. The aim of the talk is to discuss these examples, their connection to random matrix theory and computation of the correlation functions. This is a recent joint work with Alexei Borodin (U. Penn).

Presenter: Yakov Eliashberg, Princeton University November 11

Title: TBA November 11

Speaker: Kim Froyshev, Harvard University

Topic: TBA November 16

Presenter: H. Oh, Princeton University

Topic:Atoms in neutron star magnetic fields: High B asymptotics at fixed Z November 17

Presenter: Jakob Yngvason, University of Vienna

Presenter: Yakov Eliashberg, Princeton University November 18

Title: TBA November 18

Presenter: Ronnie Lee, Yale University

Topic: A differential analogue of Kummer theory on semi-abelian varieties November 23

Presenter: D. Bertrand, Paris

Presenter: Yakov Eliashberg, Princeton University November 25

Topic: Grace-like polynomials December 1

Presenter: David Ruelle, I.H.E.S.

Presenter: Yakov Eliashberg, Princeton University December 2

Title: TBA December 2

Presenter: Feng Luo, Rutgers University

Topic: TBA December 7

Presenter: William Fulton, Unviersity of Michigan

Topic: Constructive criteria for localization in random operators December 8

Presenter: Michael Aizenman, Princeton University

Presenter: Yakov Eliashberg, Princeton University December 9