Title: A Gallavotti-Cohen Type Fluctuation Theorem for Stochastic Dynamics October 14

Presenter: Herbert Spohn, Technical University, Munich

Topic: Expository Talk on P=? NP October 14

Presenter: Edward Nelson, Princeton University

Topic: Coloring graphs with sparse neighborhoods October 15

Presenter: Benny Sudakov, Tel Aviv University

Abstract: It is shown that the chromatic number of any graph with maximum degree d in which every vertex is in at most d^2/f triangles is at most O(d/log f). This is tight (up to a constant factor) for all admissible values of d and f. (Joint work with N. Alon and

M. Krivelevich)

Topic: Spectra of elements in the group ring of SU(2) October 15

Presenter: Alex Gamburd, Princeton University

Topic: Study of admissible representations of reductive p-adic groups in October 15

terms of their restriction to suitable compact-open subgroups

Presenter: Gopal Prasad, University of Michigan and IAS

Abstract: I will describe my joint work with Allen Moy in which we have introduced the notion of an "unramified type"

and proved that any admissible irreducible representation contains one and any two contained in the same irreducible

representation are "associates" of each other. This allows us to define a nonnegative rational valued invariant, called the

"depth", of an irreducible representation. Extending the work of Armand Borel on representations with vectors fixed under

an Iwahori subgroup, we can give a complete description of the representations of depth zero. We are currently looking

at how to classify representations of positive depth. We have some geometric ideas which may be of use. If time permits,

I will describe these ideas.

Topic: Complex Hyperbolic Ideal Triangle Groups October 15

Presenter: R. Schwartz, University of Maryland

Topic: On the finiteness of torsion subschemas of Hilbert-Blumenthal October 15

abelian varieties

Presenter: Jordan Ellenberg, Princeton University

Topic: On a fourth order PDE in conformal geometry October 15

Presenter: Alice Chang, Princeton University & UCLA

Paul Yang, Princeton University & USC

Topic: Extremal hemitian metrics in Riemann Surfaces October 16

Presenter: Xiuxiong Chen, Princeton University

Topic: Digraph Minors October 19 Math Building

Presenter: Paul Seymour, Princeton University

Abstract: The "graph minors" project was very fruitful, with all kinds of nice results. But what about digraphs, is there any hope of an analogue of the graph minors theorems for digraphs? What is a minor of a digraph anyway? How hard is it to test if one digraph is a minor of another? Is there such a thing as the treewidth of a digraph?

Some desirable things are not true, but others are true and provable; and some (even nicer) things can be conjectured. This talk is a survey of preliminary investigations into these questions, partly joint with Matt DeVos, Thor Johnson, Bruce Reed, Neil Robertson and Robin Thomas.

Topic: Singular affine fibrations and Fourier Integral Operators October 19

Presenter: Michael Ruzhansky, John Hopkins

Topic: Vortex Dynamics for Conservative Ginzburg-Landau Systems October 19

Presenter: Robert Jerrard, University of Illinois

Abstract: We present a rigorous analysis of the behavior of quantized vortices in solutions of the Gross-Pitaevsky equation, which is used as a model for certain kinds of superfluid Helium. We prove that, when the equation is considered in two space dimensions with appropriate initial data, the vortices behave in the incompressible limit exactly like classical fluid dynamical point vortices. We will also discuss similar results for a related nonlinear wave equation.

Topic: Anderson Localization: Results, Conjectures, and Open Problems October 21

Presenter: Werner Kirsch, University of Bochum

Topic: Geometric Algorithims and Random Walks October 22

Presenter: Miklos Simonovits, Mathematical Institute of the Hungarian

Academy of Sciences

Abstract: In the talk I will consider high dimensional convex bodies given by oracles. It is natural to try to calculate

precisely or approximately) geometric characteristics of such convex bodies, like their volume or their diameter.

Calculating volume is also connected strongly with uniform point generation in a convex body, integration, ... The basic

methods rely heavily on the theory of random walks.) I will survey various problems and results connected to:

(a) the impossibility of calculating the volume of a high dimensional convex body efficiently, using deterministic algorithms.

(b) the possibility of this by randomized algoriths. (The first result in this field, a breakthrough, was a randomized

approximation algorithm of Dyer, Frieze and Kannan. The best volume algorithm today is that of Kannan, Lovasz and

myself, providing a good estimate, using roughly O(n^5) oracle questions.

(c) randomized algorithms for diameter do not work. Diameter cannot be estimated well, even if we use randomization.

Some of the results are joint with Laszlo Lovasz, some with Kannan and Lovasz, and some with Brieden, Gritzmann,

Kannan, Klee and Lovasz; and I intend also to speak about many further results of ours and others.

Topic: On some heuristic and rigorous asymptotic formulas in the October 22

theory of disordered systems

Presenter: L. Pastur, University VII, Paris

Topic: Euler-Poincare pairings and elliptic representations October 22

of Weyl groups and p-adic groups

Presenter: Mark Reeder, Boston College

Abstract: Schneider and Stuhler have defined a pairing EP between representations of a p-adic group G, that reflects the

geometry of elliptic conjugacy classes in G. We define more elementary pairings for representations of Weyl groups W

and component groups of centralizers, and show how all these pairings are related to one another. This leads on the one

hand to explicit calculations of EP, and on the other hand, to new results about Springer representations of W.

Topic: Monopoles and the relation between 4-manifold invariants October 22

Presenter: Paul Feehan, Institute for Advanced Studies

Topic: The construction of global surfaces of section in three-dimensional October 22

dynamical systems via first order elliptic systems

Presenter: Helmut Hofer, Courant Institute, NYU

Topic: On fine properties of eigen values of analytic matrix functions

Presenter: Michael Goldstein, University of Toronto

Topic: Towards a Siege-Weil formula in exceptional groups October 22

Presenter: Wee Teck Gan, Princeton University and IAS

Topic: Counting gradient flow lines and the Seiberg-Witten October 23

Invariant of 3-manifolds

Presenter: Yi-Jen Lee, Princeton University

Topic: Critical metrics for the determinant of the laplacian October 26

Presenter: Kate Okikiolu, University of California San Diego

Topic: The Unruh Effect October 28

Presenter: Jakob Yngvason, Physics Dept., University of Vienna

Topic: A family of combinatorial determinants October 29

Presenter: Herb Wilf, University of Pennsylvania

Abstract: We evaluate a family of combinatorial determinants in simple closed form. The family includes, for example, the

nxn matrix whose (i,j) entry is the number of representations of the integer i as a sum of j squares, and many others.

Topic: Spectra of Markov operators on some countable subgroups of the

"$ax+b$"-group October 29

Presenter: Alain Valette, University of NeufChatel

Topic: Reformulations of surgery conjecture: surfaces in October 29

Topological 4-manifolds

Presenter: Slava Krushkal, Institute for Advanced Studies

Topic: Reflection on the history of PDE November 5

Presenter: Felix Browder, Rutgers University

Topic: Functions of bounded higher variation

Presenter: Robert Jerrard, University of Illinois, Urbana

Topic: Dynamical Systems

Dates: January 29, 30, & 31, 1999

Presenters: D. Dolgopyat, University of California, Berkley; G. Forni, Princeton University; V. Kaloshin, Princeton

University; Y. Katznelson, Stanford University; D. Kosygin, NY University, Courant Institute; I. Krichever, Columbia

University; M. Lyubich, SUNY Stony Brook; G. Margulis, Yale University; J. Milnor, SUNY Stony Brook; D. Ornstein,

Stanford University; M. Shub, IBM, T.J. Watson Research Labs; J. Smillie, Cornell University; W. Veech, Rice University;

J. Xia, Northwestern University

For more info or to register contact: I.Sinai or J. Mather at dona@princeton.edu or L. Neuwirth at lpn@ccr-p.ida.org

(609)279-6231.