Week of October 23 - October 25, 2002
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).
Arnold's Diffusion
Topic: Mather variational approach to Arnold's diffusion Part I of III (Part II will be October 28; Part III will be October 30)
Presenter: Jeff Xia, Northwestern University
Date: Wednesday, October 23, 2002, Time: 4:00 p.m., Location: Fine Hall 601
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
Arnold's Diffusion
Topic: The Palais-Smale condition for the time-free functional
Presenter: Gonzalo Contreras, CIMAT, Mexico
Date: Thursday, October 24, Time: 3:00 p.m., Location: Fine Hall 110
Special
Number Theory and Topology Seminar *** Please note special
day, time, and location
Topic:
On the (co-)homology of real and complex hyperbolic arithmetic manifolds
Presenter:
Nicolas Bergeron, Orsay, France
Date:
Thursday, October 24, 2002, Time:
3:30
p.m., Location: Fine Hall 214 Abstract:
We state new conjecture, of Lefschetz type, on the relationships between the (co-)homology of
real and complex hyperbolic arithmetic manifolds and their totally geodesic subspaces.
We prove particular cases of these conjectures by relating them to conjectures jointly made with L. Clozel on the automorphic
spectrum of real and complex hyperbolic arithmetic manifolds which appear to be particular cases of the Arthur conjecture and to which we
give some new approximations.
Joint
Princeton University/IAS Number Theory Seminar
Topic:
Strong Asai transfer to GL(4) via the Langlands-Shahidi method Presenter:
Muthu Krishnamurthy, IAS Date:
Thursday, October 24, 2002: Time: 4:30, Location: Fine Hall
322 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.
Arnold's Diffusion
Topic: Mather variational approach to Arnold's diffusion Part II
Presenter: Jeff Xia, Northwestern University
Date: Monday, October 28, 2002, 4:00 p.m., Fine Hall 322
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
Arnold's Diffusion
Topic: Mather variational approach to Arnold's diffusion Part III
Presenter: Jeff Xia, Northwestern University
Date: Wednesday, October 30, 2002, Time: 4:00 p.m., Location: Fine Hall 601
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, Graduate Center, CUNY
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,
Ecole Normale Superieure de Lyon
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:
Some problems on entire arithmetic functions
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: 4:30p.m.,
Location: Fine Hall 314
Week of November 18 - November 22, 2002
Analysis Seminar
Topic: Non-linear Fourier analysis and Scattering Transform in $L^2(\R)$.
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 November 25 - November 29, 2002
Analysis
Seminar Topic: General relativity constraint equations : Their elliptic
solution and their hyperbolic conservation laws
Presenter:
James W. York, Cornell University
Date:
Monday, November 25, 2002, Time: 4:00 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
Analysis Seminar
Topic: TBA
Presenter: Vincent Moncrief, Yale University
Date: Monday, December 9, 2002, Time: 4:00 p.m., Location: Fine Hall 314
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