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: The Dirichlet problem for the subLaplacian November 9

Presenter: Luca Capogna

Abstract: Consider the operator L obtained as a sum of squares of vector fields satisfying Hormander's finite rank

condition. In a joint work with N. Garofalo and D-M Nhieu we studied the dirichlet problem Lu=0, u=g on the boundary

(g continuous or in Lp), for a smooth domain D. Assuming the analogue of the Poincare outer ball condition and a

generalization of Jerison and Kenig's NTA properties we show that the Green function is Lipschitz up to the boundary and

that there is a Poisson Kernel and a representation formula. We also prove reverse Holder estimates for the Poisson

Kernel and consequently that the harmonic measure and the surface measure are mutually absolutely continuous.

Examples of domains satisfying the required properties have been constructed.

Topic: Burgers Turbulence in $d$ Dimensions November 9

Presenter: Stanislav Boldyrev, Plasma Physics Laboratory of Princeton University

Abstract: The randomly driven Navier-Stokes equation without pressure in $d$-dimensional space is considered as a

model of strong turbulence in a compressible fluid. Under the very general physical assumption of Galilean and scaling

invariance, and a particular form of the operator product expansion for the dissipative term, a closed equation is derived

for the velocity-gradient probability density function (PDF). The asymptotics of this function are found for the case of the

gradient velocity field (Burgers turbulence), and numerical solutions are provided for one-, two-, and three-dimensional

cases. Comparison with direct numerical simulations for the one-dimensional case is presented. In the one-dimensional

case, the velocity-difference PDFs are also discussed. It is shown that the phenomenon of intermittency is related to the

algebraic decay of the obtained PDFs.

Topic: TBA November 10

Presenter: David Harbater, University of Pennsylvania

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

Topic: Transfer by Markovian Flows November 12

Presenter: Leonid Koralov, Institute for Advanced Studies

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: 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: Functions of bounded n-variation November 17

Presenter: Mete Soner, 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: KAM Theorem and Quantum Field Theory November 18

Presenter: Antti Kupiainen, University of Helsinki

Topic: TBA November 18

Presenter: N. 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: TBA November 19

Presenter: Persi Diaconis, Stanford University

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: TBA 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