September
Geometric Analysis Seminar
Topic: Spectral Zeta Functions
Presenter: Kate Okikiolu, UC San Diego
Date:
Friday, September 13, 2002, Time: 3:00 p.m., Location: Fine Hall 314
Analysis Seminar
PLEASE NOTE TIME CHANGE
Topic: Existence for free boundary problems for fluids using the Nash-Moser technique
Presenter: Hans Lindblad, UC San Diego
Date:
Tuesday, September 17, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Statistical Mechanics Seminar
Topic: The ground state of the Bose gas, Part I
Presenter: Elliott Lieb, Princeton University
Date: Wednesday, September 18, 2002, Time: 2:00 p.m., Location: Jadwin 343
Abstract:
Some basic facts about the bose gas will be presented. This is the
first of several lectures leading up to the proof of Bose-Einstein condensation
in trapped gases.
PACM Colloquium
Topic: A Computational Approach to Drosophila Development and Transcriptional Control
Presenter: John Reinitz, the University at Stony Brook
Date: Monday, September 23, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:
The central problem in animal development is the generation of body form.
This problem was first considered by Aristotle, and in the nineteenth century
it was shown that basic body form is determined by interactions among cells
in a morphogenetic field. The determination of a morphogenetic field in
development involves the expression of genes in spatial patterns.
Spatially controlled gene expression cannot as yet be assayed in microarrays,
but certain special properties of the fruit fly Drosophila which make it
a premier system for developmental genetics also enable it to be used as
a naturally grown differential display system for reverse engineering networks
of genes. In this system we can approach fundamental scientific questions
about development as well as certain computational questions that arise
in the analysis of genomic level gene expression data. We approach
this problem by constructing dynamical models of the pattern formation
process, which can be formulated as systems of ordinary or partial differential
equations. These equations are then fit to gene expression data by a large-scale
optimization process. Finally, the results are used to gain new insight
into the biological system. Each of these components of the work involves
computational mathematics, which I will discuss.
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.
October
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
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.
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
PACM Colloquium
Topic: TBA
Presenter: Zhilin Li, North Carolina State University
Date:
Monday, October 14, 2002, Time: 4:00 p.m., Location: Fine Hall 214
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
PACM Colloquium
Topic: TBA
Presenter: Michael Weinstein, Bell Laboratories
Date:
Monday, October 21, 2002, Time: 4:00 p.m., Location: Fine Hall 214
November
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.
Geometric Analysis Seminar
Topic: TBA
Presenter: Hubert Bray, MIT
Date:
Friday, November 8, 2002, Time: 3:00 p.m., Location: Fine Hall 314
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
December
PACM Colloquium
Topic: TBA
Presenter: Natalia Berloff, University of Cambridge
Date:
Monday, December 2, 2002, Time: 4:00 p.m., Location: Fine Hall 214