Week of November 6 - November 8, 2002
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: Setpair formulations for Discrete Optimization
Presenter: Santosh Vempala, MIT
Date: Thursday, November 7, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Setpair formulations, first studied by Frank and Jordan, are integer programs with variables that are the edges of a graph, and constraints that bound the number of edges between pairs of subsets of vertices of the graph. In this talk we will describe the structure of the linear programming relaxation and use it to derive approximation algorithms for vertex connectivity problems (which elude the more standard set formulations), A classical theorem of Mader will play a key role in the rounding algorithm. Joint work with Joseph Cheriyan (Waterloo) and Adrian Vetta (McGill).
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: Fine Hall
322
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:
Holomorphic disks and knot invariants
Presenter:
Peter Ozsvath, Columbia University
Date:
Thursday, November 7, 2002: Time: 4:30
p.m., Location: Fine Hall 314
Abstract:
I will describe some recent work with Zoltan Szabo in which we define Floer homology groups for knots. For knots in
the three-sphere, the generators of the chain complex have an explicit combinatorial description
in terms of the planar projection of the knot, although the differentials in general are quite elusive (counting holomorphic disks in symmetric
powers of a Heegaard surface). However, this information already suffices to determine the knot homology of many knots, including all alternating
knots, and several additional families. Applications of these results include: restrictions on the Alexander polynomials of alternating knots,
obstructions for knots admitting Seifert fibered surgeries, and restrictions on the algebraic topology of smooth four-manifolds which
bound $+1$-surgery along the knot.
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: Analysis on manifolds with a Lie structure at infinity
Presenter: Victor Nistor, Pennsylvania State University
Date: Monday, November 11, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: A certain aproach to boundary value problems on polyhedral domains leads to the study of similar problems, but on non-compact manifolds. These manifolds fit into the class of `manifolds with a Lie structure at infinity,' which I will define in my talk. A manifold with a Lie structure at infinity enjoys many analytic properties similar to the analytic properties of Euclidean spaces or of compact manifolds. Examples of such manifolds also arise in scattering theory, in the study of automorphic forms, and in the study of the N-body problem.
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 *** Please note change in time
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: 2:00 p.m. and
3:00 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: Boundedness of Log Fano pairs of boundex index
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
Statistical Mechanics Seminar
Topic: The Scott correction to the energy of atoms via a new coherent state representation
Presenter: Bernhard Bodmann, Princeton University
Date: Wednesday, November 13, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract: In this talk a recent result by Solovej and Spitzer (math-ph/0208044) will be outlined. They were able to give a new proof of the Scott correction to the Thomas-Fermi energy asymptotics of large atoms, which is less technical than the original one. Their method uses a generalized coherent-state representation that they invented and which is potentially of general interest.
Department Colloquium
Topic: Partial differential equations methods for weak KAM theory
Presenter: Craig Evans, University of California at Berkeley
Date: Wednesday, November 13, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: PDE theory provides weak solutions of certain nonlinear first-order equations which, formally at least, induce simplifying changes of variables for Hamiltonian dynamics. I will discuss an ongoing program to make some part of this observation rigorous, and will in particular explain connections with Mather's variational principle for Lagrangian dynamics and Fathi's ``weak KAM'' theory.
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: Fine Hall
322
Topology
Seminar *** Please note change in time
Topic:
The Hyperbolic Solid Tube Parameter Space
Presenter:
Robert Meyerhoff, Boston College
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
Statistical Mechanics Seminar
Topic: Semiclassical Statistical Physics
Presenter: Carlos Aragao, Universidade Federal do Rio de Janeiro
Date: Wednesday, November 20, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract: We will review the use of semiclassical path-integral methods in Statistical Physics, with emphasis on applications to Quantum Statistical Mechanics and Quantum Statistical Field Theory. We will present calculations of thermodynamic quantities for the anharmonic oscillator in contact with a heat bath, for interfaces in binary mixtures (or domain walls in magnetic systems) near criticality, and for scalar fields at finite temperature.
Department Colloquium
Topic: Dimers and amoebas
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
Topology
Seminar *** Please note change in time
Topic:
Link homology
Presenter:
Mikhail Khovanov, University of California at Davis
Date:
Thursday, November 21, 2002: Time: 4:30p.m.,
Location: Fine Hall 314
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
PACM
Colloquium
Topic:
TBA
Presenter:
Michael Celia,
Department of Civil and Environmental Engineering, Princeton University
Date:
Monday, November 25, 2002, Time: 4:00 p.m., Location: Fine Hall 214
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:
Ending laminations and the classification of hyperbolic 3-manifolds
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
Topology
Seminar *** Please note change in time
Topic:
Negative curvature and exotic smooth surfaces
Presenter:
Tom Farrell, State University of New York at Binghamton
Date:
Thursday, December 12, 2002: Time: 4:30p.m.,
Location: Fine Hall 314