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Geometric Scattering Theory and Elliptic Theory on Noncompact and Singular Spaces May 07, 2001 - May 11, 2001
Registration Deadline: May 11, 2001 about 23 years ago
To apply for Funding you must register by: February 07, 2001 over 23 years ago
Parent Program:
Organizers Tanya Christiansen, Charles Epstein, Rafe Mazzeo, Richard Melrose

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As part of the Spring 2001 program on Spectral Invariants, MSRI will host a one-week workshop on Geometric Scatttering Theory and Elliptic Theory on Noncompact and Singular Spaces. This workshop will focus on problems of a scattering theoretic nature for geometric operators on manifolds with asymptotically regular geometries, and also on spectral theory and related questions of invertibility of such operators on singular spaces. The emphasis will be on the consideration of new problems and the dissemination of new techniques. Topics will include: scattering theory on manifolds with geometric structure at infinity scattering theory in the presence of stratified media propagation of singularities for solutions of the wave equation on the complement of obstacles with singularities the asymptotic distribution of resonances, and connections with the geometry at infinity L^2 and Hodge cohomology for complete and singular spaces index and elliptic theory on manifolds with corners and on stratified spaces index theory for non-classically elliptic operators, e.g. sub-elliptic operators in the Heisenberg calculus index theory for Fourier integral operators behaviour of global spectral-theoretic invariants under various types of geometric degeneration nonlinear elliptic asymptotic boundary problems FUNDING APPLICATION DEADLINE: March 26, 2001                      
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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May 07, 2001
09:30 AM - 11:00 AM
  Spectral properties of finite-volume negatively-curved manifolds
John Lott (University of California, Berkeley)
11:00 AM - 02:00 PM
  Propagation and diffraction at conic singularities
Jared Wunsch (Northwestern University)
02:00 PM - 03:00 PM
  An index theorem for manifolds with generalized fibred cusps
Boris Vaillant
May 08, 2001
09:30 AM - 11:00 AM
  Einstein metrics with prescribed conformal infinity on 4-manifolds
Michael Anderson (State University of New York, Stony Brook)
11:00 AM - 02:15 PM
  Conformal geometry, Einstein metrics and scattering
C. Graham
02:15 PM - 03:15 PM
  On LeBrun's positive frequency conjecture
Olivier Biquard (École Normale Supérieure)
May 09, 2001
09:30 AM - 11:00 AM
  The Xi function and Dirichlet-to-Neumann operator
Gilles Carron (Université de Nantes)
11:00 AM - 02:15 PM
  L2 cohomology of a convex cocompact hyperbolic manifold and the Hausdorff dimension of its limit set
Xiaodong Wang
02:15 PM - 03:15 PM
  Discreteness of spectrum and strict positivity for magnetic Schrödinger operators
Michael Shubin
May 10, 2001
09:30 AM - 11:00 AM
  Index and degeneration for the Heisenberg calculus
Richard Melrose (Massachusetts Institute of Technology)
11:00 AM - 02:15 PM
  The Cauchy-Riemann equations in balls of varying dimensions
Laszlo Lempert
02:15 PM - 04:00 PM
  Scattering theory for symbolic potentials of order zero
Andras Vasy (Stanford University)
04:00 PM - 05:00 PM
  Local index formulae for pseudo-Hermitian manifolds through non-commutative geometry
Raphael Ponge
May 11, 2001
09:30 AM - 11:00 AM
  Cyclic homology and singular varieties
Jean-Paul Brasselet
11:00 AM - 02:15 PM
  Some remarks on the Stokes Theorem and Hodge Theory on singular varieties
Daniel Grieser (Universität Oldenburg)
02:15 PM - 04:15 PM
  Determinants of Laplacians and compactness of isopolar sets for Riemann surfaces of infinite area
Peter Perry
04:15 PM - 05:15 PM
  Symbol calculus and local formula for index of a Fourier integral operator
Ryszard Nest