seminar

Current Seminars
updated 11/14/ 2001

As of November 14-16

Statistical Mechanics Seminar

Topic: Thomas Fermi theory for matter in strong magnetic fields at nonzero temperatures

Presenter: Jakob Yngvason, University of Vienna

Date: Wednesday, November 14, 2001, Time: 2:00 p.m., Location: Jadwin 343

Abstract: Rigorous results are presented on the validity of Thomas Fermi theory for the computation of the equation of state of matter in the surface layers of neutron stars.

Department Colloquium

Topic: Diophantine geometry over groups and the elementary theory of a free group

Presenter: Zlil Sela, Institute for Advanced Study

Date: Wednesday, November 14, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Abstract: We study the structure of sets of solutions to equations defined over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structure theory we obtain, enable us to answer some questions of A. Tarski's, and classify those finitely generated groups that are elementary equivalent to a free group. Connections with low dimensional topology, and some generalizations, extensions, and possible future directions will also be discussed.

Ergodic Theory and Statistical Mechanics Seminar

Topic: Markov operators and ergodic theorems for actions of free groups

Presenter: Alexander I. Bufetov, Princeton University

Date: Thursday, November 15, 2001, Time: 2:00 p.m., Location: Fine 224

Abstract: A measure-preserving action of a free group on a probability space can be considered as a stationary Markov process. This approach allows to give a short proof of the Nevo-Stein theorem and to obtain more general ergodic theorems for actions of free groups.

Discrete Mathematics Seminar

Topic: The number of graphs without forbidden subgraphs

Presenter: Bela Bollobas, Memphis and Cambridge Universities

Date: Thursday, November 15, 2001, Time: 4:00 p.m., Location: Fine Hall 224

Topology Seminar

Topic: Symplectic 4-manifolds with Kodaira dimension zero

Presenter: Tian-Jun Li, Princeton University

Date: Thursday, November 15, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Princeton/IAS Number Theory Seminar

Topic: Finiteness of integral values for the ratio of two linear recurrences

Presenter: Umberto Zannier, Istit. Univ. di Architettura di Venzia, Venice and IAS

Date: Thursday, November 15, 2001, Time: 4:30 p.m., Location: IAS SH-101

Abstract: Let $F(n),G(n)$ be linear recurrences of algebraic numbers, and assume that the ratio $F(n)/G(n)$ is an algebraic integer infinitely often. In recent joint work with P. Corvaja we prove that then there exists a nonzero polynomial $P$ such that $P(n)F(n)/G(n)$ coincides with a linear recurrence in a whole arithmetical progression. This conclusion is in a sense best-possible.

Geometric Analysis Seminar

Topic: Geometry and Soliton equations

Presenter: Chuu Lian Terng, Northeastern University

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

Week of November 19-23

Coverings of 3-Manifolds Seminar **New Seminar**

Topic: Introduction to Poenaru's work

Presenter: David Gabai, Princeton University

Date: Monday, November 19, 2001, Time: 2:30 p.m., Location: Fine Hall 322

Abstract: Valentin Poenaru has announced the following result: "The universal covering space of any closed 3-manifold is simply connected at infinity." As a corollary he gets that the universal covering space of a closed irreducible 3-manifold with infinite fundamental group is R^3. This lecture and the next will provide an introduction to Po's methods. Subsequent lectures will be given by Po himself.

Analysis Seminar

Topic: TBA

Presenter: Rowan Killip, Institute for Advanced Study

Date: Monday, November 19, 2001, Time: 4:00 p.m., Location: Fine Hall 314

PACM Colloquium

Topic: Protein folding by all-atom simulations

Presenter: Yong Duan, University of Delaware

Date: Monday, November 19, 2001, Time: 4:00 p.m., Location: Fine Hall 214

Abstract: Elucidation of the mechanisms of protein folding has challenged the scientific community for decades. It has also been termed as the second half of genomics. The challenge lies at the detailed description of the processes. Our approach is to apply all-atom molecular dynamics simulations to accurately replicate the folding processes of small proteins on computer. I will discuss the status of the field and use a few examples to demonstrate how one can effectively use such an approach in the studies of protein folding.

Algebraic Geometry Seminar

Topic: Large fundamental groups and the Shafarevich Conjecture

Presenter: Bruno de Oliveira, University of Pennsylvania

Date: Tuesday, November 20, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Abstract: In the talk I will analyse the behavior under deformations of the property of a fundamental group being large. I will also talk about a weakened Shafarevich conjecture, and prove the weakned conjecture for varieties with vector bundles with negative properties satisfying some extra cohomological conditions (joint work with Fedor Bogomolov).

Statistical Mechanics Seminar

Topic: Interaction between electrons in Quantum Dots

Presenter: Boris Altshuler, Princeton University

Date: Wednesday, November 21, 2001, Time: 2:00 p.m., Location: Jadwin 343

Abstract: We will consider general properties of interacting fermions in a finite volume. We will show that in the case in which one-particle motion is chaotic the theoretical description of the system can be dramatically simplified. More precisely, the low energy behavior can be determined by a zero-dimensional Hamiltonian, which contains at most three unknown coupling constants. This Hamiltonian generates (or suggests revisiting) several problems that might be curious from the point of view of Mathematical Physics. To illustrate this Fermi-liquid-like approach we will discuss effects of the interactions, including exchange interaction and superconducting pairing, on the charge transport through Quantum Dots.

Week of November 26-30

Analysis Seminar

Topic: TBA

Presenter: Nina Zipser, MIT

Date: Monday, November 26, 2001, Time: 4:00 p.m., Location: Fine Hall 314

PACM Colloquium

Topic: TBA

Presenter: William Cook, PACM, Princeton University

Date: Monday, November 26, 2001, Time: 4:00 p.m., Location: Fine Hall 214

Algebraic Geometry Seminar

Topic: TBA

Presenter: Jordan Ellenberg, Princeton University

Date: Tuesday, November 27, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Mathematical Physics Seminar

Topic: Stable and unstable directions for nonlinear Schroedinger equations

Presenter: Horng-Tzer Yau, Courant Institute

Date: Tuesday, November 27, 2001, Time: 4:30 p.m., Location: Jadwin A06

Abstract: We consider a nonlinear Schroedinger equation in R^3 with a bounded local potential so that the linear Hamiltonian has two bound states and the eigenvalues satisfy some resonance condition. Suppose that the initial data is small and is near some nonlinear *excited* state. Then we give a sufficient condition on the initial data so that the solution of the nonlinear Schroedinger equation approaches a certain nonlinear *ground* state as the time tends to infinity. On the other hand, for certain finite codimensional subset in the space of initial data, we construct solutions converging to the excited states in both non-resonant and resonant cases.

Tuesdays Lecture Series

Topic: Quantum Information Theory Part III

Presenter: Peter Shor, AT&T

Date: Tuesday, November 27, 2001, Time: 4:30 p.m., Location: Fine Hall 110

Abstract: The classical theorem of Shannon from 1948 gives a simple formula for how much information can be sent through a communication channel. When we try to extend this formula to the quantum regime, we find that there is no longer a unique way to define channel capacity. We can define one capacity of a channel for transmitting classical information, and another for transmitting quantum information. To further complicate the situation, these quantum channel capacities can sometimes be changed by giving the sender and receiver additional capabilities which do not change classical capacity (e.g., shared entanglement or a back channel from the receiver to the sender). However, as we discuss, there do seem to be a small number of interesting quantum channel capacities, and several of them seem to be quantifiable by analogs of Shannon's formula. This is Part Three of a three part series.

Statistical Mechanics Seminar

Topic: The (log t)^{2/3} law of the two-dimensional asymmetric simple exclusion processs

Presenter: Horng-Tzer Yau, Courant Institute

Date: Wednesday, November 28, 2001, Time: 2:00 p.m., Location: Jadwin 343

Abstract: The two-dimensional asymmetric simple exclusion process will be discussed. A classic problem is to determine the diffusion coefficient for this process and we shall show that it diverges as (log t)^{2/3} to leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion processes.

Ergodic Theory and Statistical Mechanics Seminar

Topic: Statistical properties of unimodal maps (joint with C. G. Moreira)

Presenter: Artur de Melo, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

Date: Thursday, November 29, 2001, Time: 2:00 p.m., Location: Fine Hall 224

Abstract: We consider non-trivial analytic families of unimodal maps, the main example being the real quadratic family. We give a stochastic description of the dynamics of (Lebesgue) almost every non-hyperbolic parameter. To achieve this goal we control the critical orbit, showing positive Lyapunov exponent (Collet-Eckmann condition) and polynomial recurrence with exponent 1.

Discrete Mathematics Seminar

Topic: Graph Homomorphisms and Long Range Action

Presenter: Peter Winkler, Bell Labs

Date: Thursday, November 29, 2001, Time: 4:00 p.m., Location: Fine Hall 224

Topology Seminar

Topic: The virtual fundamental class for Gromov-Witten invariants

Presenter: Tom Parker, Michigan State University and Institute for Advanced Study

Date: Thursday, November 29, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Princeton/IAS Number Theory Seminar

Topic: Deformations, derived categories and orthogonal representations

Presenter: Ted Chinburg, University of Pennsylvania

Date: Thursday, November 29, 2001, Time: 4:30 p.m., Location: Fine Hall 322

Abstract: This talk will be about joint work with Frauke Bleher on two different extensions of the deformation theory of representations of a profinite group. The first of these concerns deformations of elements in the derived category of modules for the group. The second has to do with deformations of representations into a given smooth algebraic group. I'll discuss applications to the hypercohomology of abelian varieties, and to "universal" versions of the work of Serre and Frohlich on Stiefel-Whitney classes and Hasse-Witt invariants.

Geometric Analysis Seminar

Topic: Rolling stones with flat sides: all time regularity of the interface

Presenter: Panagiota Daskalopoulos, Columbia University

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

Week of December 3-7

Analysis Seminar

Topic: TBA

Presenter: Jalal Shata, Courant Institute

Date: Monday, December 3, 2001, Time: 4:00 p.m., Location: Fine Hall 314

PACM Colloquium

Topic: Lattice Boltzmann Method for fluid flows

Presenter: Shiyi Chen, Johns Hopkins University

Date: Monday, December 3, 2001, Time: 4:00 p.m., Location: Fine Hall 214

Algebraic Geometry Seminar

Topic: New examples of non-K\"ahler homotopy types

Presenter: Tony Pantev, University of Pennsylvania

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

Abstract: This is a report on a recent joint work with Ludmil Katzarkov and Bertrand Toen in which we construct new examples of homotopy types which are not realizable as complex projective manifolds. In order to carry out the construction we define new homotopy invariants of a space $X$ related to the action of its fundamental group $\pi_{1}(X,x)$ on the higher homotopy groups of the schematized homotopy type $(X\otimes {\mathbb C})^{\text{sch}}$ of $X$. When $X$ is a smooth projective variety we use the Hodge decomposition on $(X\otimes {\mathbb C})^{\text{sch}}$ to deduce restrictions on these invariants and construct explicit examples which do not satisfy these restrictions.

Department Colloquium

Topic: TBA

Presenter: Yakov Eliashberg, Institute for Advanced Study

Date: Wednesday, December 5, 2001, Time: 4:30 p.m., Location: Fine Hall 314

Ergodic Theory and Statistical Mechanics Seminar

Topic: Central limit theorem for some models of random walks in random enviroment and model of directed polymers

Presenter: Robert A. Minlos, Institute for Information Transmission Problems, Moscow

Date: Thursday, December 6, 2001, Time: 2:00 p.m., Location: Fine 224

Princeton/IAS Number Theory Seminar

Topic: On mu-Invariants of Elliptic Curves over Q

Presenter: Mak Trifkovic, Harvard University

Date: Thursday, December 6, 2001, Time: 4:30 p.m., Location: IAS SH-101

Abstract: The talk will survey some recent work on the Iwasawa mu-invariants of p-Selmer groups of elliptic curves relative to the cyclotomic Z_p-tower over Q. The guiding conjecture in the field is due to Ralph Greenberg, and asserts that any elliptic curve over Q is isogenous to one with mu-invariant zero. I will talk about what is known about this conjecture, both by way of proof and by way of computational verification, and will present some new examples of curves with mu=0.

Geometric Analysis Seminar

Topic: Effective Schottky problem

Presenter: Samuel Grushevsky, Harvard University

Date: Friday, December 7, 2001, Time: 3:00 p.m., Location: Fine Hall 314

Week of December 10-14

Analysis Seminar

Topic: TBA

Presenter: Steve Zelditch, Johns Hopkins University

Date: Monday, December 10, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Algebraic Geometry Seminar

Topic: TBA

Presenter: Ron Donagi, University of Pennsylvania