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Laplacian Eigenvalues and Eigenfunctions: Theory, Computation, Application
February 9 - 13, 2009
Organizing Committee |
Scientific Overview |
Speaker List
Application/Registration |
Contact Us
Organizing Committee
Denis Grebenkov
(École Polytechnique, Laboratoire de Physique de la Matiere Condensee)
Peter Jones
(Yale University, Mathematics)
Naoki Saito
(University of California, Davis (UC Davis), Mathematics)
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Scientific Overview
The investigation of eigenvalues and eigenfunctions of the Laplace operator in a bounded domain or a manifold is a subject with a history of more than two hundred years. This is still a central area in mathematics, physics, engineering, and computer science, and activity has increased dramatically in the past twenty years for several reasons:
- A discovery of many fascinating properties of the Laplacian eigenfunctions such as the localization in small regions of a complicated domain and scarring in quantum chaotic billiards;
- The use of Laplacian eigenfunctions as a natural tool for a broad range of data analysis tasks, e.g., dimensionality reduction of high dimensional data via diffusion maps, or analysis of fMRI data for understanding functionality of brain regions;
- The use of the underlying Laplacian eigenvalues as natural "fingerprints" to identify geometrical shapes, e.g., copyright protection, database retrieval, quality assessment of digital data representing surfaces and solids, and the related inverse spectral problems;
- The spectral analysis of the Laplace operator for a better interpretation of nuclear magnetic resonance measurements of diffusive transport, e.g., experimental determination of the surface to volume ratio in porous media through the asymptotic properties of the heat kernel;
- Numerical computation of the Laplacian eigenfunctions and eigenvalues in irregular, often multiscale domains (or sets, or graphs) that still remains a challenging problem demanding for new numerical techniques.
This workshop will be an exciting opportunity to discuss various aspects of these new or long-standing problems with experts in different fields, including mathematics, physics, biology, and computer sciences.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
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Confirmed Speakers
Bedros Afeyan
(Polymath Research, Inc.)
Carlos Alves
(Technical University of Lisbon)
Nalini Anantharaman
(École Polytechnique)
Arnd Backer
(Technishche Universtitat Dresden)
Alex Barnett
(Dartmouth College)
Gregory Beylkin
(University of Colorado, Boulder)
Alex Bronstein
(Novafora Inc.)
Krzysztof Burdzy
(University of Washington)
Fan Chung-Graham
(University of California, San Diego (UCSD))
Ronald Coifman
(Yale University)
Marcel Filoche
(École Polytechnique)
Christopher Flake
(University of Maryland)
Denis Grebenkov
(École Polytechnique)
Ilya Gruzberg
(University of Chicago)
Michel Lapidus
(University of California, Riverside (UC Riverside))
Mauro Maggioni
(Duke University)
Francois Meyer
(University of Colorado, Boulder)
Stephane Nonnenmacher
(Service de Physique Theorique CEN Saclay)
Kate Okikiolu
(University of California, San Diego (UCSD))
Martin Reuter
(Massachusetts Institute of Technology)
Naoki Saito
(University of California, Davis (UC Davis))
Bernard Sapoval
(École Polytechnique)
Pabitra Sen
(Schlumberger-Doll Research)
Alfred Stone
(Yale University)
Terence Tao
(University of California, Los Angeles (UCLA))
Maciej Zworski
(University of California, Berkeley (UC Berkeley))
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Contact Us:
Institute for Pure and Applied Mathematics (IPAM)
Attn: LE2009
460 Portola Plaza
Los Angeles CA 90095-7121
Phone: 310 825-4755
Fax: 310 825-4756
Email: 
Website:
http://www.ipam.ucla.edu/programs/le2009/
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