Current Seminars
updated 9/26/01

 

As of September 26-28

 

Statistical Mechanics Seminar 

Topic:        Spectral Analysis of Stochastic Lattice Ginzburg-Landau Models

Presenter:   Emmanuel Pereira, Rutgers University

Date:         Wednesday, September 26, 2001, Time: 2:00 p.m., Location: Jadwin 343

Abstract:   We consider the relaxation to equilibrium of solutions of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg-Landau interactions.  Using a Feynman-Kac formula we relate the stochastic problem to a quantum field theory, and then we study the low-lying spectrum of the generator of the dynamics.  We prove the existence (or absence) of bound states for d=1,2,3.  Furthermore, using a perturbative approximation, we describe the curves for the one-particle and two-particle bound state masses in terms of the noise strength and predict an interesting phenomenon: the crossover between the one-particle and the bound state masses for a certain noise intensity.

 

Ergodic Theory and Statistical Mechanics  Seminar *** Note new room location

Topic:        Quasi-linear approximations of Navier-Stokes system

Presenter:   Yakov Sinai, Princeton University

Date:          Thursday, September 27, 2001, Time: 2:00 p.m., Location: Fine Hall 224

 

Special Geometry Seminar  ***  Note day and location

Topic:        Density problem for Sobolev mappings

Presenter:   Fengbo Hang, Princeton University

Date:          Thursday, September 27,  2001, Time: 3:00 p.m., Location: Fine Hall 110

 

Week of October 1-5

 

Analysis Seminar

Topic:        Dimension-free estimates on the polynomilals and analytic functions

Presenter:   Mikhail Sodin,  Tel Aviv University

Date:          Monday, October 1, 2001, Time: 4:00 p.m.., Location: Fine Hall 314

 

PACM Colloquium

Topic:         The Fractal Central Limit Theorem in Percolation 

Presenter:   Martin Bazant, Massachusetts Institute of Technology

Date:          Monday, October 1, 2001, Time: 4:00 p.m., Location: Fine Hall 214

Abstract:    Percolation is the standard model for random connectivity in many applications such as secondary oil recovery, polymer gelation, and epidemic spreading. The key feature of the model is its "phase transition" in the infinite-system limit: Above a critical bond concentration, there is an infinite cluster of connected bonds, and below it there is not. Of course, real systems are finite, so an important quantity for applications is the size of the largest cluster, a random variable whose poorly understood distribution is the subject of this talk.  Away from the phase transition, this distribution obeys classical limit theorems for independent random variables, namely the Fisher-Tippett theorem for extremes (subcritical) and the Central Limit Theorem for sums (supercritical). In the critical regime, however, long-range correlations exist, and various unusual distributions are observed. It is argued that these distributions can be explained by a simple probabalistic model based on self-similar random sums of random variables. The limiting behavior of these sums is governed by a "Fractal Central Limit Theorem" which predicts a non-universal central region (at the scale of the mean) and universal stretched exponential tails. These predictions are in excellent agreement with numerical simulations of critical percolation on the square site lattice, as well as known properties of the Ising model and random graphs.

 

Algebraic Geometry Seminar

Topic:        Tautological rings of the moduli spaces of curves

Presenter:   Rahul Pandharipande, Princeton University

Date:          Tuesday, October 2, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:    I will talk about the Chow rings of the moduli spaces of curves. The talk will focus on conjectural Gorenstein properties and the connections to Gromov-Witten theory (joint work with C. Faber). 

Statistical Mechanics Seminar

Topic:        Stability of Matter in a non-perturbative, Relativistic Model of Quantum Electrodynamics

Presenter:   Elliott Lieb, Princeton University

Date:          Wednesday, October 3, 2001, Time: 2 p.m., Location: Jadwin 343

Abstract:    The relativistic "no pair" model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A. There are arbitrarily many electrons and fixed nuclei with charges Z. This many-body system is shown to have finite ground state energy for suitable alpha and Z if and only if one uses the positive spectral subspace of the full Dirac operator D(A) to define an electron and not the free Dirac operator D(0). This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. 

 

            Princeton/IAS/ Rutgers Number Theory Seminar

Topic:          Hecke operators and equi-distribution of integer points on a family of homogeneous varieties.

Presenter:    Hee Oh, Princeton University

Date:           Thursday, October 4, 2001, Time: 4:30 p.m., Location: Fine Hall 314 

Abstract:      Let f be a homogeneous polynomial with integer coefficients, and let V_m be the variety defined by f=m. In the early sixties, Linnik raised the problem of understanding the distribution of the integer points V_m(Z) as m tends to infinity. In complete generality it seems hopeless to attack this question, except when the number of variables of f is much bigger than the degree of f in which case the Hardy-Littlewood method can be applied.  In this talk we discuss Linnik's problem when f arises from invariant theory, explaining how the Hecke operators then play a role here.  This is a joint work with W. T. Gan.

 

Topology  Seminar

Topic:        Some three-dimensional applications of HF^+

Presenter:   Peter Ozsvath, Princeton University

Date:          Thursday, October 4, 2001, Time: 4:00 p.m., Location: TBA

 

Geometry Analysis Seminar

Topic:        Manifolds with positive curbature almost everywhere

Presenter:   B. Wilking, University of Pennsylvania

Date:          Friday, October 5, 2001, Time: 3:00 p.m., Location: Fine Hall 314

 

Week of October 8-12

 

Analysis Seminar

Topic:        TBA

Presenter:   Kenji Nakanishi, Nagoya University and Princeton University

Date:          Monday, October 8, 2001, Time: 4:00 p.m.., Location: Fine Hall 314

 

PACM Colloquium

Topic:        Disclinated states in nematic elastomers 

Presenter:   Eliot Fried, University of Illinois at Urbana-Champaign

Date:          Monday, October 8, 2001, Time: 4:00 p.m., Location: Fine Hall 214

Abstract:    We present a theory for uniaxial nematic-elastomers with variable asphericity. As an application of the theory, we consider the time-independent, isochoric extension of a right circular cylinder.  Numerical solutions to the resulting differential equation are obtained for a range of extensions. For sufficiently large extensions, there exists an isotropic core of material surrounding the cylinder axis where the asphericity vanishes and in which the polymeric molecules are shaped as spherical coils. This region, corresponding to a disclination of strength $+1$ manifesting itself along the axis, is bounded by a narrow transition layer across which the asphericity drops rapidly and attains a non-trivial negative value. The material thereby becomes anisotropic away from the disclination so that the polymeric molecules are shaped as ellipsoidal coils of revolution oblate about the cylinder radius. In accordance with the area of steeply changing asphericity between isotropic and anisotropic regimes, a marked drop in the energy density is observed. The boundary of the disclination core is associated with the location of this energy drop. For realistic choices of material parameters, this criterion yields a core on the order of $10^{-2}$ microns, which is consistent with observations in conventional liquid-crystal melts.  Also occurring at the core boundary, and further confirming its location, are sharp transitions in the behavior of the constitutively determined contribution to the deformational stress and a minimum in the pressure. Furthermore, the constitutively determined contribution to the orientational stress is completely concentrated at the core boundary.

 

Algebraic Geometry Seminar

Topic:        Rational connectedness and rational points over function fields 

Presenter:  T. Graber, Harvard University 

Date:         Tuesday, October 9, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:    I will discuss two results. The first states that a variety over the function field of a curve which is geometrically rationally connected always has a rational point.  The second result is a sort of converse to the first. It gives a necessary and sufficient condition, in terms of rationally connected subvarieties, for a family of varieties parametrized by a base B to have a section when restricted to an arbitrary curve in B.  This is joint work with J. Harris, B. Mazur, and J. Starr. 

 

Topology  Seminar

Topic:        Braids and symplectic four-manifolds with abelian fundamental group

Presenter:   Paul Seidel, Institute for Advanced Study

Date:          Thursday, October 11, 2001, Time: 4:00 p.m., Location: TBA

 

Geometry Analysis Seminar

Topic:        Boundary regularity and structure for Poincare-Einstein metrics

Presenter:   Rafe Mazzeo, Stanford University

Date:          Friday, October 12, 2001, Time; 3:00 p.m., Location: Fine Hall 314

 

Week of October 15-19

 

PACM Colloquium

Topic:         TBA 

Presenter:    Mitchell Luskin, University of Minnesota

Date:           Monday, October 15, 2001, Time: 4:00 p.m., Location: Fine Hall 214

 

Algebraic Geometry

Topic:        Higgs bundles and mirror symmetry

Presenter:   M. Thaddeus, Columbia University and IAS

Date:          Tuesday, October 16, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:    We conjecture that the moduli spaces of Higgs bundles studied by Hitchin and Simpson satisfy the requirements to be mirror partners in the sense of Strominger-Yau-Zaslow. More precisely, the moduli space with structure group G is foliated by special Lagrangian tori, and carries a flat gerbe B whose equivalence classes of trivializations on the tori can be identified with the moduli space having the dual structure group. We have verified this for G = SL(n).  Moreover, the mirror relationship leads us to suspect a relationship between the Hodge numbers of these spaces, which we have verified for G = SL(2) and SL(3).  This is joint work with Tamas Hausel. 

 

Department Colloquium
Topic:         Hypersurfaces of prescribed curvature and energy inequalities in General Relativity

Presenter:   Gerhard Huisken, Universität Tübingen
Date:          Wednesday, October 17, 2001, Time: 4:00 p.m., Location: Fine Hall 314

 

Week of October 22-26

 

PACM Colloquium

Topic:         TBA 

Presenter:    Bradley Lucier, Purdue University 

Date:           Monday, October 22, 2001, Time: 4:00 p.m., Location: Fine Hall 214

 

Algebraic Geometry

Topic:         TBA

Presenter:   Y.P. Lee, UCLA

Date:          Tuesday, October 23, 2001, Time: 4:30 p.m., Location: Fine Hall 314

 

Department Colloquium
Topic:        TBA

Presenter:  Tobias Colding, Princeton University
Date:         Wednesday, October 24, 2001, Time: 4:00 p.m., Location: Fine Hall 314

 

Geometry Analysis Seminar

Topic:        TBA

Presenter:   Tobias Colding, Princeton University

Date:          Friday, October 26, 2001, Time: 3:00 p.m., Location: Fine Hall 314

 

Week of October 29-November 2

 

PACM Colloquium

Topic:         TBA 

Presenter:    Yves Meyer

Date:           Monday, October 29, 2001, Time: 4:00 p.m., Location: Fine Hall 214

 

Week of November 5-9 

 

PACM Colloquium

Topic:         TBA 

Presenter:    Chun Liu, Penn State University 

Date:           Monday, November 5, 2001, Time: 4:00 p.m., Location: Fine Hall 214

 

Algebraic Geometry

Topic:         p-adic representations and differential equations 

Presenter:   L. Berger, Brandeis University

Date:          Tuesday, November 6, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:    I will explain how to associate objects of a differential nature to a p-adic representation. Using recent results of Andr\'e on the structure of p-adic differential equations, these constructions allow us to give a proof of Fontaine's monodromy conjecture: every "de Rham" p-adic representation is potentially semi-stable. 

 

Department Colloquium
Topic:        TBA

Presenter:   Bjorn Engquist, Princeton University

Date:         Wednesday, November 7, 2001, Time: 4:00 p.m., Location: Fine Hall 314

 

Geometry Analysis Seminar

Topic:        Singular Yamabe metrics, explosion for superprocess, and thinness

Presenter:   D. Latutin, ETH

Topic:        TBA

Presenter:   Tobias Colding, Princeton University

Date:          Friday, November 9, 2001, Time: 3:00 p.m., Location: Fine Hall 314

 

Week of November 12-16

 

Algebraic Geometry

Topic:        TBA 

Presenter:  B. de Oliveira, University of Pennsylvania

Date:         Tuesday, November 13, 2001, Time: 4:30 p.m., Location: Fine Hall 314

 

Geometry Analysis Seminar

Topic:         TBA

Presenter:    C. L. Terng, Northeastern University

Date:           Friday, November 16, 2001, Time: 3:00 p.m., Location: Fine Hall 314

 

Week of November 26-30

 

Geometry Analysis Seminar

Topic:        TBA

Presenter:   D. Panagiota, Columbia University

Date:          Friday, November 30, 2001, Time: 3:00 p.m., Location: Fine Hall 314