PLEASE
CLICK HERE FOR INFORMATION ABOUT THE SPECIAL CONFERENCE
IN HONOR OF JOHN MATHER
Week of October 16 - October 18, 2002
Statistical Mechanics Seminar
Topic: Random graphs with a positive density of triangles
Presenter: J.P. Eckmann, University of Geneva
Date: Wednesday, October 16, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract: In a study with E. Moses (Weizmann) we discovered that the graph of the World Wide Web and many other graphs occurring in the Sciences have a density of triangles which is much higher than what can be expected for a random graph. As a consequence, P. Collet and I studied the "statistical mechanics" of subsets of random graphs with a positive density of triangles. This corresponds to a theory of extremely large deviations. If time permits, I will also describe a few aspects of the work on the WWW.
Department Colloquium
Topic: On some results of Moser and of Bangert
Presenter: Paul Rabinowitz, University of Wisconsin - Madison
Date: Wednesday, October 16 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: As part of a PDE generalization of work of Aubrey and of Mather on monotone twist maps (going from 1 dimensional orbits to codimension 1 surfaces), Moser studied minimal solutions of a class of elliptic variational problems on a torus. Using nonvariational arguments, Bangert found additional solutions of heteroclinic type. We will discuss another variational approach to these questions which will yield solutions with more complex spatial dynamics.
Discrete Mathematics Seminar
Topic: Linear Phase Transition in Random Linear Constraint Satisfaction Problem
Presenter: David Gamarnik, T.J. Watson Research Center, IBM
Date: Thursday, October 17, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Please click here to view abstract
Joint
Princeton University/IAS Number Theory Seminar
Topic:
Epsilon Constants and Orthogonal Representations Presenter:
Darren Glass, Columbia University
Date:
Thursday, October 17, 2002: Time: 4:30, Location: Fine
Hall 322
Abstract:
Suppose X is an arithmetic surface and G is a finite group which acts tamely on X. We define Y to be the quotient
scheme Y and we let V be a representation of G. Associated to this information, we can define an
L-function L(Y,V,s) which satisfies a certain functional equation involving an epsilon constant. Calculating these epsilon constants is very
difficult in general, but under additional hypotheses the situation can greatly simplify. My research assumes that V is an orthogonal
representation, and in that case reduces the calculation to a calculation about how the representation acts at only a finite number of points.
Topology
Seminar ***Please note change in time
Topic:
Simple closed geodesics on surfaces.
Presenter:
Nancy Hingston, the College of New Jersey
Date:
Thursday, October 17, 2002: Time: 4:30 p.m., Location: Fine
Hall 314
Abstract:
What can one say about the simple closed geodesics on a 2-sphere with a fixed, generic metric? Easy examples show
the lengths may not be bounded. Is the Morse index bounded? We prove some results for metrics
satisfying a Kupka-Smale-type condition, and describe examples of metrics whose simple closed geodesics are "not so simple". These
include a metric for which the Morse index is unbounded. (joint work with Toby
Colding)
Geometric Analysis Seminar
Topic: On some conformally invariant fully nonlinear equations
Presenter: Yanyan Li, Rutgers University
Date: Friday, October 18, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of October 21 - October 25, 2002
Arnold's Diffusion Seminar
Topic: Solutions of the n-body problem with prescribed initial and final configurations: existence and applications
Presenter: A. Chenciner, Paris VII
Date: Monday, October 21, 2002, Time: 2:00 p.m., Location: Fine Hall 322
Arnold's Diffusion Seminar
Topic: Geometric mechanism for instability in Hamiltonian dynamics
Presenter: R. de la Llave, University of Texas at Austin
Date: Monday, October 21, 2002, Time: 4:00 p.m., Location: Fine Hall 322
Analysis Seminar
Topic: The solution of the square root problem of Kato
Presenter: Steven Hofmann, University of Missouri at Columbia
Date: Monday, October 21, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: Please click here to view abstract
PACM Colloquium
Topic: Theory and Computation of Resonances of Photonic Microstuctures
Presenter: Michael Weinstein, Bell Laboratories
Date: Monday, October 21, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Photonic crystal waveguides are a class of optical waveguides with novel transverse microstructure. A great deal of tunability of optical properties is achieved through variations in the geometry of microfeatures, their distribution and refractive index contrasts. We discuss a multiple scale approach to the study of photonic crystal waveguides. Energy escapes from the core due to a combination of propagation and tunneling. Of central importance are leaky modes (resonance states) and their associated complex effective indices (scattering resonance poles). The leading order theory agrees with classical homogenization theory, describing an effective homogeneous medium with dielectric properties given by an appropriate averaging of the refractive index profile. We compute the first non-trivial correction, which takes into account the microstructure, and find that the higher order homogenization expansion gives very good agreement with full simulations by Fourier and multipole methods. The higher order expansion is crucial for estimation of leakage rates; in various examples of physical interest, the leading order (homogenization) gives a substantial underestimation. Finally, a rigorous justification of the homogenization expansion of scattering resonances is obtained as part of a resonance perturbation theory for an appropriate "preconditioned" Lippmann-Schwinger equation.
Joint Analysis and Arnold's Diffusion Seminar
Topic: The asymptotic behavior of entropy solutions of forced burgers equations on the circle
Presenter: P. Bernard, Institut Fourier, France and EPFL, Swizerland
Date: Tuesday, October 22, 2002, Time: 1:00 p.m., Location: Fine Hall 214
Statistical Mechanics Seminar
Topic: Magnets, microchips, memories and markets; statistical physics of complex systems
Presenter: David Sherrington, Oxford University and IAS
Date: Wednesday, October 23, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract: Disorder and frustration in the interactions between even quite simple microscopic entities can lead to complex macroscopic co-operative behaviour, whose understanding has required the development of novel concepts and techniques and continues to pose challenges. In this talk an overview will be given of the origin and character of such complexity and its conceptual understanding. It will be shown how resultant concepts can be fruitfully and symbiotically transferred between systems of physically quite different appearance. Illustrations will include frustrated magnets, (spin glasses), hard optimization problems (microchip design), associative memories (as in the brain or artificial neural networks) and simple markets (inspired by economics).
Department Colloquium
Topic: Algebraic Geometry of Nash Equilibria
Presenter: Bernd Sturmfels, UC at Berkeley
Date: Wednesday, October 23, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We present an algebraic approach to Nash equilibria in game theory, along the lines of Chapter 6 in my new book "Solving Systems of Polynomial Equations" (http://math.berkeley.edu/~bernd/cbms.html). The set of all Nash equilibria of an N-person game is a real algebraic variety, which is typically a finite set. A combinatorial formula for its expected cardinality was given by the economists McKelvey and McLennan in 1997. We show how to find all Nash equilibria using computational algebraic geometry, and we present the Universality Theorem (proved by Ruchira Datta in 2002) which states that every real algebraic variety arises from a game with three players.
Discrete Mathematics Seminar
Topic: Set systems with restricted intersections
Presenter: Jacques Verstraete, Microsoft Research
Date: Thursday, October 24, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Please click here to view abstract
Topology
Seminar *** Please note change in time
Topic:
Convexity in Geometry
Presenter:
Igor Rivin, Temple University
Date:
Thursday, October 24, 2002: Time: 4:30 p.m., Location: Fine
Hall 314
Abstract:
For mysterious reasons, many of the natural sets and functions arising in geometry turn out to be convex. This is our
good fortune, since extremizing convex functions over convex sets has pleasant consequences. In this talk we will describe some
examples. It is hoped that the talk is self contained.
Geometric Analysis Seminar
Topic: Higher order parabolic equations in conformal geometry
Presenter: Simon Brendle, Princeton University
Date: Friday, October 25, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of October 28 - November 1, 2002
Special
Colloquium
Topic:
Primes is in P Presenter:
Manindra Agrawal, Kanpur, India Date:
Monday, October 28, 2002: Time: 11:00 a.m., Location: A01
McDonnell Hall Abstract:
Determining if a given
number is prime has engaged the attention of theoretical computer scientists for
several decades.
Several efforts have been made to design an efficient (in other words,
polynomial-time) algorithm.
These include Miller’s test (a polynomial-time algorithm; however, it
is correct only assuming Extended Riemann Hypothesis), Rabin’s and
Solovey-Strassen’s tests (randomized polynomial-time tests),
Adelman-Pomerance-Rumeli’s test (deterministic test requiring slightly
super-polynomial time), etc. It
has remained a major open problem to design an unconditional deterministic
polynomial-time algorithm for the problem. In this talk, we present the first
such algorithm.
Joint Analysis and Arnold's Diffusion Seminar
Topic: The interface of PDE's and Lagrangian dynamics: existence of C1 subsolutions
Presenter: Albert Fathi, ENS-Lyon, France
Date: Tuesday, October 29, 2002, Time: 1:00 p.m., Location: Fine Hall 214
Week of November 4 - November 8, 2002
Analysis Seminar
Topic: Purely Nonlinear Instability of Minimal Energy Standing Waves
Presenter: Andrew Comech, University of North Carolina
Date: Monday, November 4, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: For a variety of nonlinearities, the nonlinear Schroedinger equation is known to possess localized quasistationary solutions ("standing waves"). We prove that in the generic situation the standing wave of minimal energy among all other standing waves is unstable. This case was falling out of the scope of the classical paper by Grillakis, Shatah, and Strauss on orbital stability of standing waves. An interesting feature of the problem is the absence of (exponential) instability in the linearized system; in this sense, the resulting instability is ``purely nonlinear''. Essentially, the instability is caused by higher algebraic degeneracy of zero eigenvalue in the spectrum of the linearized system. The result can be generalized to abstract Hamiltonian systems with U(1) symmetry.
PACM Colloquium
Topic: The Forced van der Pol Equation: New Insights on an Old Problem
Presenter: John Guckenheimer, Cornell University
Date: Monday, November 4, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The forced van der Pol equation is the original example of chaos in dynamical systems. It is also an example of relaxation oscillations, periodic motions with short and fast time scales. This lecture describes joint work, primarily with Kathleen Hoffman and Warren Weckesser, to understand bifurcations of dynamical systems with multiple time scales. Using the forced van der Pol equation as a case study, we illustrate how canards - solutions that track unstable slow manifolds - play an important role in both bifurcations and chaos. In many situations canards cannot be computed by solving initial value problems, so many of the phenomena that we exhibit are missed by typical simulation studies of multiscale systems.
Joint Algebraic Geometry and Number Theory Seminar
Topic: A Mahler formula for dynamical systems on the sphere
Presenter: Lucien Szpiro, Columbia University
Date: Tuesday, November 5, 2002, Time: 4:30 p.m., Location: Fine Hall 322
Statistical Mechanics Seminar
Topic: Are electromagnetic ultraviolet cutoffs here to stay?
Presenter: Michael Kiessling, Rutgers University
Date: Wednesday, November 6, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract: There are strong indications from nonperturbative QED that its ultraviolet cutoff(s) cannot be removed. Differing expert opinions on what that could mean include (paraphrasing): a) We have not yet seen a proof that it cannot be done. b) A purely electromagnetic theory has to get into conflict with itself at high energies. A consistent theory requires a (supersymmetic) unification of all interactions. c) We have been trying to quantize the wrong classical model. d) We should stop trying to quantize a classical model and look for some radically new ideas, like non-associative algebra. Each opinion has its own merits, and it should be interesting to find out which one, if any, is correct. In my talk I will review some older results of others and present some new results of my own which, I believe, open up an entirely new perspective on the issue.
Department Colloquium
Topic: Expander graphs - where Combinatorics and Algebra compete and cooperate
Presenter: Avi Wigderson, IAS and The Hebrew University
Date: Wednesday, November 6, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Expansion of graphs can be given equivalent definitions in combinatorial and algebraic terms. This is the most basic connection between combinatorics and algebra illuminated by expanders and the quest to construct them. The talk will survey how fertile this connection has been to both fields, focusing on recent results. In particular, we'll explain the zig-zag product of graphs, how it leads to an elementary combinatorial construction of expanders, and its relation to semi-direct product in groups.
Discrete Mathematics Seminar
Topic: TBA
Presenter: Santosh Vempala, MIT
Date: Thursday, November 7, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Joint
Princeton University/IAS Number Theory Seminar
Topic:
On the sign of Kloosterman sums
Presenter:
Philippe Michel, IUF and Univ. Montpellier II
Date:
Thursday, November 7, 2002: Time: 4:30, Location: TBA
Abstract:
Let $S(1,1;n)$ be the Kloosterman sum of modulus $n$. In a joint work with E. Fouvry, we
show that, as $n$ varies over a set of allmost prime integers (ie. more precisely over the set of squarefree
integers having at most 23 prime factors) $S(1,1;n)$ takes positive (resp. negative) values infinitely often.This talk will describe the proof and some possible improvements of
this result which mixes together, sieve methods (Bombieri's or Selberg's sieve), automorphic forms
(Kloostermania) and $l$-adic techniques (Katz's vertical Sato-Tate laws for Kloosterman
sums).
Topology
Seminar *** Please note change in time
Topic:
TBA
Presenter:
Peter Ozsvath, Columbia University
Date:
Thursday, November 7, 2002: Time: 4:30 p.m., Location: Fine
Hall 314
Geometric Analysis Seminar
Topic: TBA
Presenter: Hubert Bray, MIT
Date: Friday, November 8, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of November 11 - November 15, 2002
Analysis Seminar
Topic: TBA
Presenter: Victor Nistor, Pennsylvania State University
Date: Monday, November 11, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: The Level Set Method-what's in it for you?
Presenter: Stanley Osher, University of California, Los Angeles
Date: Monday, November 11, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The level set method for capturing moving fronts was introduced in 1987 by Osher and Sethian. It has proven to be phenomenally successful as a numerical device. For example, typing in "Level Set Methods" on Google's search engine gives roughly 3200 responses. Applications range from capturing multiphase fluid dynamical flows, to special effects in Hollywood to visualization,image processing, control, epitaxial growth, computer vision and many more. In this talk we shall give an overview of the numerical technology and a few applications.
Special
Lecture
Topic:
An Introduction to Quasiconvexity (Parts I and II - see November 13 for
Parts III - VI)
Presenter:
John Ball, Oxford University and IAS
Date:
Tuesday, November 12, 2002: Time: 2:30 p.m. and 4:00 p.m., Location: Fine
Hall 110 Abstract:
Quasiconvexity is the central convexity condition of the multi-dimensional
calculus of variations, but because of the lack of an adequate characterization
of quasiconvex functions it remains somewhat mysterious. The lectures will
cover the following topics: a) Definition and examples of quasiconvex
functions. Null Lagrangians and polyconvexity. Rank-one
convexity. b) Lower semicontinuity and existence of minimizers.
Applications to elasticity. Quasiconvexity in the interior and at the
boundary as necessary conditions for a minimizer. Partial
regularity. Relaxation. c) Quasiconvexity and gradient Young
measures. Quasiconvex sets of matrices. Relaxation and the passage from
microscales to macroscales. Examples involving finitely many matrices or
energy wells. Martensitic microstructure. d) Extensions and
applications: higher-order problems, homogenization, quasiregular maps...These
lectures precede the conference Quasiconvexity and its Appications (see http://www.mis.mpg.de/conferences/quasiconvexity2002/).
The lectures will be self-contained and assume as little background knowledge as
possible. However, some familiarity with Sobolev spaces and weak
convergence in Lp spaces will be an advantage.
Geometric
Analysis Seminar ***Please note special day,
time and location Topic:
A $C^0$-theory for the blow-up of elliptic equations with critical Sobolev growth
Presenter:
Emmanuel Hebey, Université de Cergy-Pontoise
Date:
Tuesday, November 12, 2002, Time: 4:00 p.m., Location: Fine Hall 1201
Algebraic Geometry Seminar
Topic: TBA
Presenter: James McKernan, Santa Barbara
Date: Tuesday, November 12, 2002, Time: 4:30 p.m., Location: Fine Hall 322
Geometric
Analysis Seminar ***Please note special day,
time and location Topic:
Sharp local isoperimetric inequalities
Presenter:
Olivier Druet, Université de Cergy-Pontoise Date: Tuesday,
November 12, 2002, Time: 5:00 p.m., Location: Fine Hall 1201
Special
Lecture
Topic:
An Introduction to Quasiconvexity (Parts Parts III - VI, this is a
continuation of the lectures from November 12)
Presenter:
John Ball, Oxford University and IAS
Date:
Wednesday, November 13, 2002: Time: 9:00 a.m. and 11:00 a.m.,
Location: Fine Hall 1001 Abstract:
See abstract from November 12.
1:30 p.m. and 3:00 p.m. Location: Fine
Hall 322
Department Colloquium
Topic: TBA
Presenter: Craig Evans, University of California at Berkeley
Date: Wednesday, November 13, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Discrete Mathematics Seminar
Topic: TBA
Presenter: Mike Saks, Rutgers University
Date: Thursday, November 14, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Joint
Princeton University/IAS Number Theory Seminar
Topic:
TBA
Presenter:
Jonathan Pila, University of Melbourne and IAS
Date:
Thursday, November 14, 2002: Time: 4:30, Location: TBA
Topology
Seminar *** Please note change in time
Topic:
TBA
Presenter:
Mikhail Khovanov, UC Davis
Date:
Thursday, November 14, 2002: Time: 4:30
p.m., Location: Fine
Hall 314
Week of November 18 - November 22, 2002
Analysis Seminar
Topic: TBA
Presenter: Christoph Thiele, UCLA
Date: Monday, November 18, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: An Eulerian Method for Multiphase Computations of the Schrodinger Equation
Presenter: Xiantao Li, PACM, Princeton University
Date: Monday, November 18, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abtract: We present a new numerical method for the computation of the semiclassical limits of the Schrodinger equation. We first use Wigner transform technique to derive a Vlasov equation in the phase space, and then find its solution in the multiphase regime. By taking moment closure, we obtain the multiphase equations in the physical space. The numerical procedure follows the solution of the Vlasov equation, but only operates in the physical space, which offers great efficiency and simplicity. In addition, we will show some other application of this technique, such as the multivalued solutions of the Euler Poisson system in Klystron.
Algebraic Geometry Seminar
Topic: One dimensional families of Calabi-Yau threefolds
Presenter: Charles F. Doran, Columbia University
Date: Tuesday, November 19, 2002, Time: 4:30 p.m., Location: Fine Hall 322
Department Colloquium
Topic: TBA
Presenter: Andrei Okounkov, Princeton University
Date: Wednesday, November 20, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Joint
Princeton University/IAS Number Theory Seminar
Topic:
TBA
Presenter:
Gautam Chinta, Brown University
Date:
Thursday, November 21, 2002: Time: 4:30, Location:
Fine Hall 322
Geometric
Analysis Seminar
Topic:
TBA
Presenter:
Spyridon Alexakis, Princeton University
Date:
Friday, November 22, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of December 2 - December 6, 2002
Analysis Seminar
Topic: TBA
Presenter: Mihaela Iftime, Northeastern University
Date: Monday, December 2, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: TBA
Presenter: Natalia Berloff, University of Cambridge
Date: Monday, December 2, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Department Colloquium
Topic: TBA
Presenter: Haim Brezis, Rutgers University and Paris VI
Date: Wednesday, December 4, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Discrete Mathematics Seminar
Topic: TBA
Presenter: Peter Winkler, Bell Labs
Date: Thursday, December 5, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Joint
Princeton University/IAS Number Theory Seminar
Topic:
TBA
Presenter:
Ling Long, IAS
Date:
Thursday, December 5, 2002: Time: 4:30, Location:
Fine Hall 322
Topology
Seminar *** Please note change in time
Topic:
TBA
Presenter:
Yair Minsky, SUNY at Stonybrook
Date:
Thursday, December 5, 2002: Time: 4:30 p.m., Location: Fine
Hall 314
Geometric
Analysis Seminar
Topic:
TBA
Presenter:
Andrea Malchiodi, IAS
Date:
Friday, December 6, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of December 9 - December 13, 2002
Department Colloquium
Topic: TBA
Presenter: Ed Witten, Institute for Advanced Study
Date: Wednesday, December 11, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Joint
Princeton University/IAS Number Theory Seminar
Topic:
TBA
Presenter:
Yuval Flicker, Ohio State University
Date:
Thursday, December 12, 2002: Time: 4:30, Location:
Fine Hall 322