Current Seminars
updated 10/17/ 2001
As of October 17-19
Statistical Mechanics Seminar
Topic: Nonconvergent pertubative expansions for unstable invariant tori in Hamiltonian mechanics
Presenter: Giovanni Gallavotti, University of Rome
Date: Wednesday, October 17, 2001, Time: 2 p.m., Location: Jadwin 343
Abstract: We consider a class of a priori stable quasi-integrable analytic Hamiltonian systems and study the regularity of low-dimensional hyperbolic invariant tori as functions of the perturbation parameter. We show that, under natural nonresonance conditions, such tori exist and can be identified through the maxima or minima of a suitable potential. They are analytic inside a disc centered at the origin and deprived of a region around the positive or negative real axis with a quadratic cusp at the origin. The invariant tori admit an asymptotic series at the origin with Taylor coefficients that grow at most as a power of a factorial and a remainder that to any order $N$ is bounded by the $(N+1)$-st power of the argument times a power of $N!$. We show the existence of a summation criterion of the (generically divergent) series, in powers of the perturbation size, that represent the parametric equations of the tori by following the renormalization group methods for the resummations of perturbative series in quantum field theory.
Department Colloquium ***Note new time for this week only***
Topic: Hypersurfaces of prescribed curvature and energy inequalities in General Relativity
Presenter: Gerhard Huisken, Universität Tübingen
Date: Wednesday, October 17, 2001, Time: 3:30 p.m., Location: Fine Hall 314
Ergodic Theory and Statistical Mechanics Seminar
Topic: Sample path properties of the stochastic flow and the dynamics of an oil spill (joint work with Dima Dolgopyat and
Vadim Kaloshin) Part I
Presenter: Leonid Koralov, Princeton University
Date: Thursday, October 18, 2001, Time: 2:00 p.m., Location: Fine 224
Abstract: We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi point motion. An application of these results allows us to describe the limiting shape of a domain in $\R^2$ (say, an oil spill on the surface of the ocean) carried by the stochastic flow. This lecture will continue on October 25, 2001.
Discrete Mathematics Seminar
Topic: Triangulated spheres and colored cliques
Presenter: Maria Chudnovsky, Princeton University
Date: Thursday, October 18, 2001, Time: 4:00 p.m., Location: Fine Hall 224
Topology Seminar
Topic: An invariant of homology cobordism
Presenter: Nikolai Saveliev, University of Miami and Princeton University
Date: Thursday, October 18, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Geometric Analysis Seminar
Topic: Minimizing Oseen-Frank energy: a geometric approach
Presenter: M. Giaquinta, Scuola Normale Superiore
Date: Friday, October 19, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of October 22-26
PACM Colloquium
Topic: Wavelet Methods for Medical Tomography
Presenter: Bradley Lucier, Purdue University
Date: Monday, October 22, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The mathematics of Computed Tomography (CT) and Positron Emission Tomography (PET) medical imaging is based on inverting the Radon transform. The Radon transform is a linear, smoothing operator, so its inverse, while linear, is unbounded, and the presence of noise (especially for PET imaging) makes applying this inverse problematic. David Donoho introduced Wavelet Shrinkage applied to Wavelet-Vaguelette decompositions to solve this problem. This talk describes how Donoho's method can be cast in a variational framework, how to choose the scaling of shrinkage parameters, and gives experimental results that compare our method with the so-far standard method, Filtered Back Projection.
Algebraic Geometry
Topic: Quantum cohomology on flag manifolds, finite difference Toda lattices, and quantum groups
Presenter: Y.P. Lee, UCLA
Date: Tuesday, October 23, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A "completely integrable" system, the finite difference Toda lattices, is constructed from quantum groups $U_q(g)$ for any complex simple Lie algebras $g$ by defining a homomorphism from the center of $U_q(g)$ to finte difference operators. The image consists of the commuting hamiltonians of the finite difference Todalattices. (This part will only be briefly sketched.). We will prove that a generating function of one-point quantum $K$-invariants, the $J$-function, on (complete) flag manifolds of type $A_r$ is the common eigenfunction of the commutating hamiltonians. We also conjecture that this statement holds for arbitrary simple Lie algebra. This is based on the joint work with A. Givental in math.AG/0108105. If time permits, I will also discuss some problems in quantum $K$-theory in general, and how this result could be related to the quantum $K$-ring by a "Floer $K$-theory"
Mathematical Physics Seminar
Topic: Delocalization in Random Polymer Chains
Presenter: Gunter Stolz, University of Alabama at Birmingham
Date: Tuesday, October 23, 2001, Time: 4:30 p.m., Location: Jadwin A06
Tuesdays Lecture Series
Topic: Quantum Information Theory Part I
Presenter: Peter Shor, AT&T
Date: Tuesday, October 23, 2001, Time: 4:30 p.m., Location: Fine Hall 110
Abstract: When quantum computers were first proposed, it was widely believed that large-scale quantum computing would be infeasible, because it appeared impossible to correct errors on a quantum computer without disturbing the state of, and thus invalidating, the computation. Quantum error correcting codes were invented to circumvent this difficulty; these codes can be used to correct any likely error in an encoded quantum state without disturbing the state. Surprisingly, these codes are connected to the first application of the strange properties of quantum mechanics to computer science, namely the 1984 quantum cryptography protocol of Bennett and Brassard. It took over a decade to rigorously prove that this protocol was secure against an eavesdropper, and the first proofs were quite complicated. Recently, John Preskill and I found a simple proof by relating the security of the Bennett and Brassard key distribution protocol to the efficacy of CSS (Calderbank-Shor-Stean) codes, a class of quantum error correcting codes. In this talk, I introduce the fundamentals of quantum error correction and show their relationship to quantum key distribution. This is Part One of a three part series.
Department Colloquium
Topic: Embedded minimal surfaces in 3-manifolds
Presenter: Tobias Colding, Princeton University
Date: Wednesday, October 24, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: I will discuss the description of the space of all embedded minimal surfaces in a 3-manifold. (This is joint work with Bill Minicozzi).
Ergodic Theory and Statistical Mechanics Seminar
Topic: Sample path properties of the stochastic flow and the dynamics of an oil spill (joint work with Dima Dolgopyat and
Vadim Kaloshin) Part II
Presenter: Leonid Koralov, Princeton University
Date: Thursday, October 25, 2001, Time: 2:00 p.m., Location: Fine 224
Abstract: We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi point motion. An application of these results allows us to describe the limiting shape of a domain in $\R^2$ (say, an oil spill on the surface of the ocean) carried by the stochastic flow. This is a continuation of the talk from Thursday, October 18, 2001.
Discrete Mathematics Seminar
Topic: Local density in graphs with forbidden subgraphs
Presenter: Peter Keevash, Cambridge University and Princeton University
Date: Thursday, October 25, 2001, Time: 4:00 p.m., Location: Fine Hall 224
Topology Seminar
Topic: TBA
Presenter: Thomas Parker, Institute for Advanced Study
Date: Thursday, October 25, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Geometric Analysis Seminar
Topic: Estimates for embedded minimal disks
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: Cell Communication Networks in Drosophila Oogenesis: Models and Analysis
Presenter: Stanislav Shvartsman, Chemical Engineering, Princeton University
Date: Monday, October 29, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Week of November 5-9
PACM Colloquium
Topic: Complex fluids: liquid crystals, mixtures and polymeric materials
Presenter: Chun Liu, Penn State University
Date: Monday, November 5, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: In this talk, several dynamical systems modeling specific types of complex fluids are introduced. The relation between these and other existing models will be discussed. We will also study the relations between the variational procedure; the basic energy law; stability; and the higher order energy estimates. The different non-Newtonian properties such systems exhibit is of particular interest. Finally we will study a differential-integral equation system that allows us to consider couplings and interactions of different spatial length scales.
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.
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: TBA
Presenter: Bjorn Engquist, Princeton University
Date: Wednesday, November 7, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Geometric Analysis Seminar
Topic: Singular Yamabe metrics, explosion for superprocess, and thinness
Presenter: D. Labutin, 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
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
Topic: TBA
Presenter: V. Vatsal, University of British Columbia
Date: Tuesday, November 13, 2001, Time: 4:30 p.m., Location: Fine Hall 314
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.
Geometric 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 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
Topic: TBA
Presenter: B. de Oliveira, University of Pennsylvania
Date: Tuesday, November 20, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Week of November 26-30
Mathematical Physics Seminar
Topic: Stable and unstable directions for nonlinear Schroedinger equations
Presenter: H.T. 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.
Geometric Analysis Seminar
Topic: TBA
Presenter: Panagiota Daskalopoulos, Columbia University
Date: Friday, November 30, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of December 3-7
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
Topic: TBA
Presenter: T. 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
Week of December 10-14
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