Topic: On the Stability of positive Molecular Ions November 11

Presenter: Rafael Benguria, Catholic University, Santiago, Chile

Topic: Regularity of harmonic maps November 11

Presenter: Sun-Yung Alice Chang, Princeton University

Abstract: Harmonic maps are critical points of the energy functional in between manifolds. Existence and regularity

properties of the map have been a subject of intensive study in geometric analysis. A remarkable result of Helein in 1990

establishes that any weak harmonic map defined on a compact surface is already smooth. The original proof of Helein

replies on a compensated compactness result of Coifman-Lions-Meyer-Semmes, which in turn is a consequence of

duality of H^1 amd BMO. In this talk, I will survey results in the field, give a simplier proof of the result of Helein when

the target manifold of the map is spheres and indicate the extension of the regularity results to bi-harmonic maps.

Topic: Lower bounds on code invariants November 12

Presenter: Alexander Barg, Bell Labs (Lucent Technologies)

Abstract: This talk deals with a new application of Delsarte's linear programming method to obtaining lower bounds on

invariants of codes related to their distance enumerator. The method proves useful in a variety of asymptotic problems of

coding and information theory.

Topic: Transfer by Markovian Flows November 12

Presenter: Leonid Koralov, Institute for Advanced Studies

Topic: Hecke algebras and weights of Markov traces November 12

Presenter: Rosa Orellana, University of California, San Diego

Topic: Weyl Curvature, Einstein Metrics, and the Seiberg-Witten Equations November 12

Presenter: Claude LeBrun, SUNY at Stony Brook

Topic: Divisibility of class numbers and sieve techniques November 12

Presenter: Etienne Fouvry, Universite d'Orsay

Topic: Homology associated to a contact form on the space of dual Legendrian curves November 13

Presenter: Abbas Bahri, Rutgers University

Topic: Shape and Morse theory of attractors November 16

Presenter: Lev Kapitanskii, Kansas State

Topic: Geostrophic Turbulence and Poleward Heat Flux in the Atmosphere November 16, 1998

Presenter: Isaac Held, Geophysical Fluid Dynamics Laboratory/NOAA and

Program in Atmospheric and Oceanic Sciences Princeton University

Abstract: A common difficulty in the study of turbulent transport is the absence of any separation between the scale of the

energy containing eddies and the scale of the inhomogeneity of the turbulence. (Think of heat transport in Benard

convection or momentum mixing across the turbulent flow through a pipe.) As a result intuitive concepts such as mixing

lengths and turbulent diffusion have limited utility, and it is difficult to relate studies of homogeneous turbulence to questions

about turbulent fluxes.

A distinctive kind of turbulence occurs in the atmosphere and the oceans, on scales large enough that the vorticity is a

small departure from the vorticity of solid body rotation (flows with small Rossby number). In the atmosphere, the

energy-containing eddies of this "geostrophic turbulence" are the cyclones and anticyclones familiar from weather maps,

with a typical horizontal scale of 1000 km. The heat transported by these eddies determines the north-south temperature

gradient on our Earth. In the oceans, the geostrophic eddy scale is smaller (10 -100 km), so these eddies are much more

difficult to account for by direct numerical simulation, and their role in global ocean circulation is a key unsolved problem.

In this seminar I describe an idealized model of geostrophic turbulence designed to shed light on the parameters that

control poleward heat transport in the atmosphere. In this model, there IS a natural scale separation between the eddies

and the external forcing. Therefore, one can design a homogeneous framework in which to measure the "turbulent

diffusivity" of the medium. Numerical results show how well this diffusivity accounts for the fluxes in a simple

inhomogeneous problem of interest. Most of the seminar will then be devoted to a scaling argument for the

diffusivity. This theory depends on an elaboration of the picture of energy and enstrophy cascades in two-dimensional

turbulence. It suggests that the poleward heat flux in the atmosphere is proportional to the fourth power of the

north-south temperature gradient.

Topic: Functions of bounded n-variation November 17

Presenter: Mete Soner, Princeton Univeristy PACM

Abstract: In this talk, I will define and study the properties of a class of functions whose generalized Jacobian is a Radon

measure. This class of functions, called BnV, is the extension of the classical BV space for vector valued functions.

Motivation for introducing BnV comes from a class of variational problems with codimension two singularities; model

example is the Ginzburg-Landau functional for a superconducting material. Main mathematical results are the extension of

the Fleming-Rishel co-area formula, and the extension of the DeGiorgi rectifiability result which states that the essential

boundary of a set of finite perimeter has a tangent plane.

Topic: Generalized Newton Polygons as lattice points November 17

Presenter: Ching-Li Chai, University of Pennsylvania

Abstract: Let p be a prime number. Let G be a reductive algebraic group over Q which is quasi-split over Qp. Let X be

a G(R)-conjugacy classes of R-homomorphisms from ResC/RGm to G, so that (G, X) defines a Shimura variety. Let

N(G,X)Z be set of generalized Newton polygons which are expected to appear in the F-crystal attached to the Shimura

variety Sh(G, X). The set N(G,X)Z has a natural partial ordering related to specialization of F-isocrystals. We give an

explicit description of this set N(G, X)Z using the weights and roots. The main result is that N(G, X)Z is ranked as a

partially ordered set, that is any two maximal chains have the same length. There is a simple formula which computes the

length of its segments. These results gives a prediction of the dimension of the Newton strata of the reduction of Sh(G, X)

at primes over p. Relation with the recent purity theorem for the Newton stratification due to de Jong and Oort will also

be explained.

Topic: KAM Theorem and Quantum Field Theory November 18

Presenter: Antti Kupiainen, University of Helsinki

Topic: On the size of complete minimal surfaces November 18

Presenter: Nikolai Nadirashvili, University of Chicago

Topic: MAXCUT in triangle-free graphs November 19

Presenter: Noga Alon, IAS and Tel Aviv University

Abstract: We obtain sharp bounds for the minimum possible size of a maximum cut in triangle-free graphs with m edges.

These are derived by combining probabilistic techniques with algebraic tools and character-sum estimates, and improve

previous results of various researchers.

Topic: Random products of matrices, sharp ergodic theorems, and distributing November 19

points uniformly on measure spaces

Presenter: Yehuda Shalom, Princeton University

Topic: An application of Kostant's work on Lie algebra cohomology November 19

to a problem in astronomy

Presenter: Persi Diaconis, Stanford University

Abstract: Statistical analysis of red shift data leads to the problem of generating random permutations with restricted

positions. For one common censorship pattern the problem can be solved using Hanlon's adaption of Kostant's seminal

work on Lie algebra cohomology. For other censorship patterns new methods are required.

This is joint work with R. Graham.

Topic: TBA November 19

Presenter: R. Fintushel, Michigan State University

Topic: TBA November 19

Presenter: Jean Bourgain, Institute for Advanced Study

Topic: Period functions associated to Maass waveforms and spectral theory November 19

on the modular surface

Presenter: John Lewis, Framingham State College

Topic: Uniqeness of Kahler-Ricci solitons November 20

Presenter: Gang Tian, MIT

Topic: The conjugacy problem in the braid groups November 23

Presenter: Joan Birman, Barnard College/Columbia University

Topic: TBA November 23

Presenter: Michael Goldstein, Toronto

Topic: Zeros of Graph-counting Polynomials November 25

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

Topic: TBA November 30

Presenter: Michael Koluntzakis, Urbana-Champaign

Topic: Statistical Mechanics and the Eigenvalue Density of Random Matrices December 2

Presenter: Michael Kiessling, Rutgers University

Topic: TBA December 3

Presenter: Haim Brezis, Rutgers University and Universite Paris VI

Topic: Integrability and selection in non-linear interface dynamics December 9

Presenter: Mark Mineev-Weinstein, Los Alamos National Laboratory