Week of September 24 - 27, 2002
Algebraic Geometry Seminar
Topic: Independence of ell of monodromy groups
Presenter: CheeWhye Chin, UC, Berkeley
Date: Tuesday, September 24, 2002, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: If G is a connected reductive groups over the field of complex numbers, let Reps(G) denote the set of isomorphism classes of its irreducible representations. Given two such groups, say G and G' , can we tell if they are isomorphic from detail knowledge of Reps(G) and Reps(G') ? I will explain that with enough "details", the answer is yes. The method can be applied to address certain questions of the independence of ell of monodromy groups.
Statistical Mechanics Seminar
Topic: The ground state of the Bose gas, Part II
Presenter: Robert Seiringer, Princeton University
Date: Wednesday, September 25, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract: We continue the investigation of the dilute Bose gas. We study the ground state of N interacting particles in a trap, and show that in the dilute limit it shows complete Bose-Einstein condensation. The condesate wave function is determined by minimizing the Gross-Pitaevskii functional. We also prove superfluid behavior of the system.
Discrete Mathematics Seminar
Topic: Independence number and complete graph minor
Presenter: Ken-ichi Kawarabayashi, Keio and Princeton University
Date: Thursday, September 26, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Please click here to view abstract
Geometric Analysis Seminar
Topic: Perron's method for second order semilinear wave equations
Presenter: Penelope Smith, Lehigh University
Date: Friday, September 27, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of September 30 - October 4, 2002
Analysis Seminar
Topic: Construction of solutions to the Yang-Mill Equations in higher dimensions
Presenter: Simon Brendle, Princeton University
Date: Monday, September 30, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: The Level Set Method and Schroedinger's Equation
Presenter: Li-Tien Cheng, University of California, San Diego
Date: Monday, September 30, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The level set method has recently been succesfully applied to the construction wavefronts in geometrical optics. We extend the approach here to wavefronts found in Schroedinger's equation as well as other quantities of interest. Advantages such as an Eulerian foundation and the ability to handle multivaluedness are preserved in the extension.
Celestial Mechanics Seminar
Topic: Capture Processes and Chaotic Motions in Celestial Mechanics Part I
Presenter: Edward Belbruno, PACM
Date: Tuesday, October 1, 2002, Time: 11:00 a.m., Location: Fine Hall 1001
Abstract: We discuss two types of topics, which present some recent results. One is on a proof which unifies two types of seemingly unrelated capture processes in the three-body problem. This is accomplished by proving that a hyperbolic invariant set exists on a stability transition region called a weak stability boundary. This boundary has interesting applications, and the hyperbolic invariant set is related to unbounded(parabolic motion). The set more generally is proven to exist by Xia. In another unrelated topic we prove that Aubrey-Mather sets exist in the three-body problem near special periodic orbits. Part II will be on Tuesday, October 8, 2002.
Department Colloquium
Topic: Compatibility, microgeometry and materials
Presenter: John Ball, Oxford University and IAS
Date: Wednesday, October 2, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Please click here to view abstract
Discrete Mathematics Seminar
Topic: Extremal set-systems with restricted k-wise intersections
Presenter: Benny Sudakov, Princeton University
Date: Thursday, October 3, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Please click here to view abstract
Arnold's Diffusion Seminar
Topic: Survey of results on Arnold diffusion
Presenter: Jeff Xia, Northwestern University
Date: Thursday, October 3, 2002, Time: 3:00 p.m., Location: Fine Hall 110
Geometric Analysis Seminar
Topic: The Dirichlet problem for minimal surface systems
Presenter: Mu-Tao Wang, Columbia University
Date: Friday, October 4, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of October 7 - October 11, 2002
Analysis Seminar
Topic: Proof of the Double Bubble Conjecture
Presenter: Frank Morgan, Williams College
Date: Monday, October 7, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: The Double Bubble Conjecture says that the familiar double soap bubble is the least-area way to enclose and separate two given volumes of air. I'll discuss the proof, the latest results, and open questions.
PACM Colloquium
Topic: Wave localization and guidance in photonic bandgap structures
Presenter: Fadil Santosa, University of Minnesota
Date: Monday, October 7, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Photonic bandgap structures are anticipated to play an important role in the development of devices for optical communication. These nano-structures are made of material with periodic index of refraction. Defects are introduced to guide and manipulate light. In this talk, the speaker will provide an introduction to photonic bandgap structures, and the mathematical tools needed to analyze them. Major ideas are illustrated with numerical examples. Some of the open problems will be described.
Celestial Mechanics Seminar
Topic: Capture Processes and Chaotic Motions in Celestial Mechanics Part II
Presenter: Edward Belbruno, PACM
Date: Tuesday, October 8, 2002, Time: 11:00 a.m., Location: Fine Hall 1001
Abstract: We discuss two types of topics, which present some recent results. One is on a proof which unifies two types of seemingly unrelated capture processes in the three-body problem. This is accomplished by proving that a hyperbolic invariant set exists on a stability transition region called a weak stability boundary. This boundary has interesting applications, and the hyperbolic invariant set is related to unbounded(parabolic motion). The set more generally is proven to exist by Xia. In another unrelated topic we prove that Aubrey-Mather sets exist in the three-body problem near special periodic orbits.
Algebraic Geometry Seminar
Topic: Rational families of vector bundles on curves
Presenter: Ana-Maria Castravet, IAS
Date: Tuesday, October 8, 2002, Time: 4:30 p.m., Location: Fine Hall 322
Department Colloquium
Topic: Nonlinear PDE's in Conformal Geometry
Presenter: Sun-Yung A. Chang, Princeton University
Date: Wednesday, October 9, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Discrete Mathematics Seminar
Topic: TSP cuts that do not follow the template paradigm
Presenter: Vasek Chvatal, Rutgers University
Date: Thursday, October 10, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Please click here to view abstract
Geometric Analysis Seminar
Topic: Conformal maps, convex hulls and Kleinian groups
Presenter: Chris Bishop, SUNY at Stony Brook
Date: Friday, October 11, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of October 14 - October 18, 2002
Analysis Seminar
Topic: TBA
Presenter: Natasa Pavlovic, Princeton University
Date: Monday, October 14, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: Theoretical and Numerical Analysis for Some Non-linear Interface Problems
Presenter: Zhilin Li, North Carolina State University
Date: Monday, October 14, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:
Non-linear partial differential equations with discontinuity in the coefficient have many
applications. In this talk, I will focus on two different non-linear interface problems. One is the
potential equation for magneto-rhological (MR) fluid that contains metal particles. The
permeability is discontinuous across the interface between the fluid and the particles. The
second problem is the weighted minimal surface problem. We have generalized the Sneil's law
for optical path to the three dimensional weighted minimal surface problem. Numerically, we use
the substitution method to solve the non-linear PDE. Since the coefficient of the potential
equation depends on the gradient of the solution, we use the maximum preserving immersed
interface method coupled with multigrid solvers to solve the linearized problems. Numerical
examples will also be presented.
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
Analysis Seminar
Topic: TBA
Presenter: Steven Hofmann, University of Missouri at Columbia
Date: Monday, October 21, 2002, Time: 4:00 p.m., Location: Fine Hall 314
PACM Colloquium
Topic: TBA
Presenter: Michael Weinstein, Bell Laboratories
Date: Monday, October 21, 2002, Time: 4:00 p.m., Location: Fine Hall 214
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
Geometric Analysis Seminar
Topic: TBA
Presenter: Simon Brendle, Princeton University
Date: Friday, October 25, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of November 4 - November 8, 2002
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
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
PACM Colloquium
Topic: TBA
Presenter: Stanley Osher, University of California, Los Angeles
Date: Monday, November 11, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Algebraic Geometry Seminar
Topic: TBA
Presenter: James McKernan, Santa Barbara
Date: Tuesday, November 12, 2002, Time: 4:30 p.m., Location: Fine Hall 322
Discrete Mathematics Seminar
Topic: TBA
Presenter: Mike Saks, Rutgers University
Date: Thursday, November 14, 2002, Time: 2:15 p.m., Location: Fine Hall 224
Geometric Analysis Seminar
Topic: TBA
Presenter: Emmanuel Hebey, Université de Cergy-Pontoise
Date: Friday, November 15, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Week of November 18 - November 22, 2002
PACM Colloquium
Topic: TBA
Presenter: Xiantao Li, PACM, Princeton University
Date: Monday, November 18, 2002, Time: 4:00 p.m., Location: Fine Hall 214
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
Week of December 2 - December 6, 2002
PACM Colloquium
Topic: TBA
Presenter: Natalia Berloff, University of Cambridge
Date: Monday, December 2, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Discrete Mathematics Seminar
Topic: TBA
Presenter: Peter Winkler, Bell Labs
Date: Thursday, December 5, 2002, Time: 2:15 p.m., Location: Fine Hall 224