Current Seminars
updated 3/13/ 2002
As of March 13 - 15, 2002
Discrete Mathematics Seminar
Topic: Separating random points
Presenter: Van Vu, University of California, San Diego
Date: Thursday, March 14, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Ergodic Theory and Statistical Analysis Seminar
Topic: Topological shocks and Lagrangian minimizers
Presenter: Konstantin Khanin, Newton Institute, Cambridge
Date: Thursday, March 14, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Joint Princeton University/IAS/Rutgers University Non-Linear Analysis Seminar
Topic: Global existence and convergence for a fourth order flow in conformal geometry
Presenter: Simon Brendle, University of Tuebingnon
Date: Thursday, March 14, 2002, Time: 4:00, Location: Fine Hall 214
Joint Princeton University/Rutgers University Topology Seminar
Topic: Aspects of rigidity for mapping class groups and automorphism groups of free groups
Presenter: Martin Bridson, Imperial College London/Columbia
Date: Thursday, March 14, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Princeton University/IAS Number Theory Seminar
Topic: Pro-l birational anabelian geometry
Presenter: Florian Pop, University of Bonn and the Institute for Advanced Study
Date: Thursday, March 14, 2002, Time: 4:30, Location: IAS SH-101
Abstract: The ``yoga'' of anabelian geometry is that under certain ``anabelian hypothesis'' arithmetic and geometry are encoded in Galois theory. There are mainly two points of view: The functorial one and the constructive one. We will explain how an infinite finitely generated field is ``encoded'' in its pro-l Galois theory; hence, how it can be reconstructed from its pro-l Galois theory (where l is a prime different from the characteristic).
Graduate Student Seminar
Topic: Fractional-moment methods for continuum Schr\"odinger operators
Presenter: Jeff Schenker, Princeton University
Date: Friday, March 15, 2002, Time: 1:00 p.m., Location: Fine Hall 1001
Abstract: I will describe the phenomena of Anderson localization and its relevance to physics and present a new technique for analyzing localization phenomena which occur with continuum Schr\"odinger operators. The technique is an extension of the Aizenman-Molchanov method for discrete operators.
Geometric Analysis Seminar
Topic: On the Singular Set of J-holomorphic Maps
Presenter: Tristan Riviere, ETH (Swiss Federal Institute of Technology, Zurich)
Date: Friday, March 15, 2002, Time: 3:00 p.m., Location: Fine Hall 314
March 18 - 22, 2002
PACM Colloquium
Topic: Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives
Presenter: Chi-Wang Shu, Brown University
Date: Monday, March 18, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: In this talk I will present recent results on developing local discontinuous Galerkin methods for solving time dependent partial differential equations containing third spatial derivatives (KdV type equations), containing fourth spatial derivatives (time dependent bi-harmonic type equations) and containing fifth spatial derivatives. For these new methods we present correct interface numerical fluxes and prove $L^2$ stability for a quite general class of nonlinear problems. These methods are especially suitable for the "convection dominated" cases, namely when the coefficients in front of the higher order derivatives are small or vanishing in certain parts of the domain and the nonlinear first derivative terms dominate. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for equations with first derivatives and tested for equations with second derivatives, on equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh. This is joint work with Jue Yan.
Mathematical Physics Seminar *** Please note change in date from February 26, 2002
Topic: The Cauchy Problem for a Dynamical Euler Elastica
Presenter: Almut Burchard, University of Virginia
Date: Tuesday, March 19, 2002, Time: 4:30 p.m., Location: Jadwin A06
Abstract: We consider the dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives, and a second order elliptic equation for its tension. Local existence and uniqueness of solutions are established for sufficiently regular initial data. This is joint work with L.E. Thomas.
Joint Princeton University/IAS/Rutgers University Non-Linear Analysis Seminar
Topic: Interaction functionals for hyperbolic systems of conservation laws
Presenter: Alberto Bressan, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Italy
Date: Thursday, March 21, 2002, Time: 4:00, Location: Fine Hall 214
Abstract: For strictly hyperbolic systems of conservation laws in one space dimension, global existence of entropy weak solution was proved in a classical paper of Glimm (1965). The construction of solution is here based on a compactness argument, where the total oscillation (i.e. the BV norm) is controlled by a suitable interaction functional. Very recently, wave interaction functionals have been introduced also in connection with viscous perturbations of hyperbolic systems, not necessarily in conservation form. This allows the construction of unique "viscosity solutions" to nonlinear hyperbolic systems, continuously depending on the initial data. The talk will also discuss the possibility of a-priori BV bounds (in terms of similar interaction functionals) for other types of approximations, such as relaxations or finite-difference numerical schemes.
March 25 - 29, 2002
Analysis Seminar
Topic: Singular maximal functions near L^1
Presenter: Andreas Seeger, University of Wisconsin
Date: Monday, March 25, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: Flash & Turn: Self-organization and dynamics of fireflies and ants
Presenter: Bard Ermentrout, University of Pittsburgh
Date: Monday, March 25, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Many species of insects are able to organize global patterns and solve a variety of computationally intersting problems by using local sensory cues. In this talk, I will focus on two examples: (i) synchronous flashing in Southeast Asian fireflies and (ii) trail formation in army ants. I will suggest that many of the individual-level strategies used to accomplish these tasks are analagous to those used at the single neuron level. I will show that the synchronous flashing of fireflies uses a mechanism like spike-time dependent plasticity. I also show that models for the formation of ant trails are similar to those used in Hebbian learning. Thus, trails that are used are strengthened and those which are not are weakened.
Algebraic Geometry Seminar
Topic: A p-adic local monodromy theorem
Presenter: Kiran Kedlaya, University of California, Berkeley
Date: Tuesday, March 26, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A conjecture of R. Crew, motivated by work of Dwork et al, states that any differential equation on a p-adic annulus with a "Frobenius structure" is quasi-unipotent, i.e., has a nilpotent basis on some finite unramified cover of the annulus. I'll make this assertion more precise, outline briefly some proofs of the conjecture, and mention some applications (finite dimensionality of p-adic cohomology, a conjecture of Fontaine on p-adic Galois representations).
Discrete Mathematics Seminar
Topic: A trace bound for the discrepancy
Presenter: Bernard Chazelle, Princeton University
Date: Thursday, March 28, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Ergodic Theory and Statistical Analysis Seminar
Topic: Strange nonchaotic attractors
Presenter: Arkady Pikovsky, Universitat Potsdam
Date: Thursday, March 28, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: I discuss states that appear in nonlinear quasiperiodically forced systems and are from one hand non-chaotic (the largest Lyapunov exponent is negative) and from another hand are fractal objects. Two approaches to characterize these sets are discussed: one is based on the rational approximations of the quasiperiodic forcing, another is based on the calculation of finite-time Lyapunov exponents. I show that in some cases the strange nonchaotic attractors have singular continuous spectra. Several situations are described, where the onset of strange nonchaotic attractors can be characterized vie the renormalization group method.
Princeton University/IAS Number Theory Seminar *** Please note special time
Topic: Ramified Triple Product Identities
Presenter: Thomas Watson, UCLA
Date: Thursday, March 28, 2002, Time: 4:00 p.m., Location: Fine Hall 322
Geometric Analysis Seminar
Topic: TBA
Presenter: Bruce Kleiner, University of Michigan & Courant Institute of Mathematics
Date: Friday, March 29, 2002, Time: 3:00 p.m., Location: Fine Hall 314
April 1-5, 2002
PACM Colloquium
Topic: Some themes of feedback control theory, and their relevance to systems molecular biology
Presenter: Eduardo Sontag, Rutgers University and Princeton University
Date: Monday, April 1, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Algebraic Geometry Seminar
Topic: p-adic Fourier Theory and Lubin-Tate theory
Presenter: Jeremy Teitelbaum, University Illinois at Chicago.
Date: Tuesday, April 2, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: In this talk I will discuss some new results (joint with Peter Schneider) on p-adic integration that generalize old results of Amice and Lazard. Let $L$ be a finite extension of Qp$. We study the space of locally L-analytic functions on the ring of integers $o=o_L$, and its dual, the ring of locally $L$-analytic distributions. We show that this ring of distributions is isomorphic to the global functions on a rigid space $\hat{o}$ parameterizing $L$-analytic characters of $o$. The space $\hat{o}$ turns out to be quite interesting; if $L$ is not Q_p $\hat{o}$ isomorphic over C_{p}$ to the open unit disk, but is not a disk over any discretely valued extension of $L$. Our methods rely on Lubin-Tate theory and some results from Tate's classic paper on p-divisible groups. I will also explain how these results allow one to construct a p-adic L-function for a CM elliptic curve at a supersingular prime. Such functions have been discussed by Katz and by Boxall, but our results allow one to approach the construction using "Coleman power series" in a manner that is formally identical to that used for ordinary primes as described, for example, in deShalit's book.
Mathematical Physics Seminar
Topic: Tunneling on Quantum Graphs
Presenter: Pavel Exner, Theor. Physics, Czech Academy of Science, Prague
Date: Tuesday, April 2, 2002, Time: 4:30 p.m., Location: Jadwin A06
Department Colloquium
Topic: Evolution of Language
Presenter: Stephen Smale, University of California at Berkeley
Date: Wednesday, April 3, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A mathematical model is presented which helps to understand how languages are formed. A theorem in this setting is the convergence to a common language under a hypothesis on linguistic encounters.
Discrete Mathematics Seminar
Topic: Electrical Circuit Theory Generalized to Matroids
Presenter: Alan Sokal, New York University
Date: Thursday, April 4, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Ergodic Theory and Statistical Analysis Seminar
Topic: Bernoulli diffeomorphisms with non-zero exponents on any manifold
Presenter: Yakov Pesin, Penn State University
Date: Thursday, April 4, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: In the talk I will describe a solution of a long-standing problem to construct a Bernoulli diffeomorphism with nonzero Lyapunox exponents on any compact smooth Riemannian manifold.
April 8 - 12, 2002
Analysis Seminar
Topic: TBA
Presenter: Diego Cordoba, Princeton University
Date: Monday, April 8, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Algebraic Geometry Seminar
Topic: TBA
Presenter: Joseph Silverman, Brown University
Date: Tuesday, April 9, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Department Colloquium
Topic: TBA
Presenter: Michael Rabin, Harvard University
Date: Wednesday, April 10, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Joint Princeton University/IAS/Rutgers University Non-Linear Analysis Seminar
Topic: $L_p$-bounds on curvature and rectifiability of singular setsy
Presenter: Jeff Cheeger, Courant Instititue, NYU
Date: Thursday, April 11, 2002, Time: 4:00, Location: Fine Hall 214
Princeton University/IAS Number Theory Seminar
Topic: Galois groups and geometry of modular varieties
Presenter: Alexander Goncharov, Brown University
Date: Thursday, April 11, 2002, Time: 4:30, Location: TBA
Geometric Analysis Seminar
Topic: TBA
Presenter: Rina Rotman, University of Toronto and the Courant Institute of Mathematics
Date: Friday, April 12, 2002, Time: 3:00 p.m., Location: Fine Hall 314
April 15 - 19, 2002
PACM Colloquium
Topic: TBA
Presenter: Christodolous Floudas, Chemical Engineering, Princeton University
Date: Monday, April 15, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Algebraic Geometry Seminar
Topic: TBA
Presenter: Alexander Braverman, Harvard University
Date: Tuesday, April 16, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Mathematical Physics Seminar *** Please note change in date from March 19, 2002
Topic: TBA
Presenter: Jakob Yngvason, University of Vienna
Date: Tuesday, April 16, 2002, Time: 4:30 p.m., Location: Jadwin A06
Discrete Mathematics Seminar
Topic: TBA
Presenter: Tibor Szabo, ETH Zurich
Date: Thursday, April 18, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Geometric Analysis Seminar
Topic: Bifurcations of $J$-holmorphic maps
Presenter: Tom Parker, Michigan State University and the Institute for Advanced Study
Date: Friday, April 19, 2002, Time: 3:00 p.m., Location: Fine Hall 314
April 22 - 26, 2002
Analysis Seminar
Topic: The lost proof of Loewner's theorem
Presenter: Barry Simon, Caltech
Date: Monday, April 22, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: A real-valued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem.
PACM Colloquium
Topic: TBA
Presenter: Ken Church, AT&T Labs - Research
Date: Monday, April 22, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Mathematical Physics Seminar
Topic: Sum Rules and Spectral Properties of Jacobi Matrices
Presenter: Barry Simon, Caltech
Date: Tuesday, April 23, 2002, Time: 4:30 p.m., Location: Jadwin A06
Discrete Mathematics Seminar
Topic: Partitions with bounded components
Presenter: Penny Haxell, University of Waterloo
Date: Thursday, April 25, 2002, Time: 2:00 p.m., Location: Fine Hall 224
April 29 -May 3, 2002
PACM Colloquium
Topic: TBA
Presenter: Herb Keller, California Institute of Technology
Date: Monday, April 29, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Department Colloquium **** Rescheduled from March 6, 2002 ****
Topic: Mathematical problems suggested by Analog-to-Digital conversion
Presenter: Ingrid Daubchies, Princeton University
Date: Wednesday, May 1, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: In Analog-to-Digital conversion, continuously varying functions (e.g. the output of a microphone) are transformed into digital sequences from which one then hopes to be able to reconstruct a close approximation to the original function. The functions under consideration are typically band-limited (i.e. their Fourier transform is zero for frequencies higher than some given value, called the bandwidth); such functions are completely determined by samples taken at a rate determined by their bandwidth. These samples then have to be approximated by a finite binary representation. Surprisingly, in many practical applications one does not just replace each sample by a truncated binary expansion; for various technical reasons, it is more attractive to sample much more often and to replace each sample by just l or –1, chosen judiciously. In this talk, we shall see what the attractions are of this quantization scheme, and discuss several interesting mathematical questions suggested by this approach. This will be a review of work by many others as well as myself, including Ron DeVore, Sinan Gunturk, Thao Nguyen and Ozgur Yilmaz. It is also a case study of how continuous interaction with engineers helped to shape and change the problems as we tried to make them more precise.
Discrete Mathematics Seminar
Topic: TBA
Presenter: Igor Pak, MIT
Date: Thursday, May 2, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Princeton University/IAS Number Theory Seminar
Topic: TBA
Presenter: Brooks Roberts, University of Idaho
Date: Thursday, May 2, 2002, Time: 4:30, Location: TBA