Topic: The Unruh Effect October 28

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

Topic: Geometric flows of parabolic type October 28

Presenter: H. Mete Soner; PACM and CEOR Princeton

Abstract: Essential behavior of solutions to a large class of parabolic equations can be captured their singular set. In

models for phase separation the singular set is a domain wall, in the Ginzburg-Landau model for superconductivity or in

liquid crystals, the defect set has codimension two. There are applications to hydrodynamic limit of interacting particle

models as well.

In this talk, I will outline the "recent" weak theories for the evolution of these singular sets and use them to develop an

asymptotic theory for a class of reaction diffusion equations. Related topics are: viscosity solutions of Crandall, Evans

and Lions, geometric flows of Almgren and Taylor, and level set theory of Evans-Spruck and Chen-Giga-Goto.

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 October 29

"$ax+b$"-group

Presenter: Alain Valette, University of NeufChatel, Switzerland

Abstract: Paraphrasing M. Kac, Gromov asked "Can you hear the shape of a group?"; i.e., given a Cayley graph

associated with a finitely generated group $\Gamma$, which information can one extract from the spectrum of the

adjacency operator acting on $\ell^{2}(\Gamma)$? In the first part of the talk, we survey results on this inverse spectral

problem.

Since there are relatively few exact computations of such spectra, we address in the second part the direct spectral

problem for the subgroup $\Gamma_{n}$ of the $ax+b$ group, generated by translation by $1$ and dilation by $n$.

Using C*-algebraic techniques, we present computations both for the directed and undirected Cayley graphs of

$\Gamma_{n}$. In the directed case, one of the computations depends on the Generalized Riemann Hypothesis (actually

on Artin's conjecture).

Topic: Reformulations of surgery conjecture: surfaces in October 29

topological 4-manifolds

Presenter: Slava Krushkal, Institute for Advanced Studies

Topic: Recent development on compact Homogenous space October 30

Presenter: Zhuang-dan Guan, Princeton University

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: Functions of bounded n-variation November 10

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: 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: Transfer by Markovian Flows November 11

Presenter: Leonid Koralov, Institute for Advanced Studies

Topic: Regularity of harmonic maps November 11

Presenter: Sun-Yung Alice Chang, Princeton University

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: R. 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: TBA November 13

Presenter: Abbas Bahri, Rutgers University

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