Current Seminars
updated 11/6/ 2001
As of November 6-9
Algebraic Geometry Seminar
Topic: p-adic representations and differential equations
Presenter: Laurent 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.
Tuesdays Lecture Series
Topic: Quantum Information Theory Part II
Presenter: Peter Shor, AT&T
Date: Tuesday, November 6, 2001, Time: 4:30 p.m., Location: Fine Hall 110
Abstract: We discuss entanglement, the property of quantum mechanics that Einstein called "spooky action at a distance." Entanglement between two parties is what leads to the violation of Bell's inequality, and also it appears to be one of the properties of quantum mechanics that speeds up quantum computers. Entanglement between two parties lets them perform a number of interesting tasks, one of which is "quantum teleportation," where a quantum state can be transfered using only classical communication and entanglement. We discuss these uses of entanglement, and then discuss how to quantify it. This is Part Two of a three part series.
Department Colloquium
Topic: Numerical Homogenization
Presenter: Bjorn Engquist, Princeton University
Date: Wednesday, November 7, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Ergodic Theory and Statistical Mechanics Seminar
Topic: Classical and quantum scattering for random decaying potentials.
Presenter: Wilhelm Schlag, Institute for Advanced Study
Date: Thursday, November 8, 2001, Time: 2:00 p.m., Location: Fine 224
Discrete Mathematics Seminar
Topic: Approximately Covering by Cycles in Planar Graphs
Presenter: Bruce Reed, McGill University
Date: Thursday, November 8, 2001, Time: 4:00 p.m., Location: Fine Hall 224
Topology Seminar
Topic: Exceptional Lie groups and del Pezzo surfaces
Presenter: John Morgan, Columbia University
Date: Thursday, November 8, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: It has been known for a long time that there is a close relationship between the root lattices for the exceptional groups E_6, E_7, E_8 and the second cohomology group of the del Pezzo surfaces of degrees 3,2, and 1. We explore this relationship in more detail and put it on a more geometric footing -- for example we see the relationship between the 27 lines on the del Pezzo of degree 3 and the 27 dimensional minuscule representation of E_6 as well as other similar geometric/representation theory correspondences.
Princeton/IAS Number Theory Seminar
Topic: Periods, L-functions and knots
Presenter: Fernando Rodriguez-Villegas, University of Texas and Harvard University
Date: Thursday, November 8, 2001, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: Inspired by Deninger's work, David Boyd found many experimental relations between the Mahler measure of certain two variable polynomials and the zeta function of an associated number field at s=2. I will describe how these identities can be proved and the role played by the underlying hyperbolic geometry.
Geometric Analysis Seminar
Topic: Singular Yamabe metrics, explosion for superprocess, and thinness
Presenter: D. Labutin, ETH
Topic: Multi-valued minimal graphs and properness of embedded disks
Presenter: Tobias Colding, Princeton University
Date: Friday, November 9, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of November 12-16
PACM Colloquium
Topic: Eukaryotic Cell Cycle Controls: An Example of the 'Last Step' in Computational Molecular Biology
Presenter: John Tyson, Virginia Polytechnic, Institute and State University
Date: Monday, November 12, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The cell cycle is the sequence of events by which a growing cell duplicates all its components and partitions them more-or-less evenly between two daughter cells. In the last 15 years, molecular biologists have made great progress in identifying the genes, proteins and molecular interactions that control the basic events of the cell cycle (DNA synthesis and mitosis). The control system is so complex that its behavior cannot be understood by casual, hand-waving arguments. We use biochemical kinetics and dynamical systems theory to convert hypothetical molecular mechanisms of cell cycle control into quantitative computational models. By testing our models against experimental observations, we gain new insights into how the control system works. The approach is generally applicable to any complex gene-protein network that regulates some physiological characteristics of a living cell.
Algebraic Geometry Seminar
Topic: Uniform distribution of Heegner points
Presenter: Vinayak Vatsal, University of British Columbia
Date: Tuesday, November 13, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The goal of this talk is to explain how general results of Ratner's on unipotent flows on p-adic Lie groups leads to a resolution of Mazur's conjectures on elliptic curves over towers of anticyclotomic fields. The main idea is that Ratner's theorem may be used to show that the reductions of CM points are uniformly distributed on the components of a suitable Shimura curve, and that the elements of a certain Galois group act independently, in a suitable sense.
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 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.
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
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: TBA
Presenter: Bruno de Oliveira, University of Pennsylvania
Date: Tuesday, November 20, 2001, Time: 4:30 p.m., Location: Fine Hall 314
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
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.
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
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: TBA
Presenter: Tony Pantev, University of Pennsylvania
Date: Tuesday, December 4, 2001, Time: 4:30 p.m., Location: Fine Hall 314
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
Princeton/IAS Number Theory Seminar
Topic: TBA
Presenter: Mak Trifkovic, Harvard University
Date: Thursday, December 6, 2001, Time: 4:30 p.m., Location: TBA
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
Date: Tuesday, December 11, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Department Colloquium
Topic: Universal covering spaces of closed 3 manifolds are simply connected at infinity
Presenter: Valentin Poenaru, Université de Paris-Sud (Orsay)
Date: Wednesday, December 12, 2001, Time: 4:30 p.m., Location: Fine Hall 314