Workshop on Microlocal Methods in Geometric Analysis
Description
This workshop is a part of the program Microlocal Methods in Geometric Analysis and Mathematical Physics (fall 97).
This workshop was devoted to the aspects of geometric analysis and partial differential equations in which microlocal methods (or more generally "phase space techniques") have been or are becoming useful. The specific topics included:
- geometric scattering theory
- eigenvalue asymptotics and "quantum chaos" on manifolds
- degenerate elliptic boundary value problems
- geometric study of hyperbolic equations
In conjunction with the workshop Professor R.B. Melrose of Massachusetts Institute of Technology delivered series of lectures as part of the Fields Institute Distinguished Lecture Series.
Schedule
| 08:55 to 09:00 |
Director's Address
D.Dawson |
| 09:00 to 09:50 |
Traces on certain algebras of pseudodifferential operators
V. Guillemin |
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Heat asymptotics for singular problems
J. Bruening |
| 11:20 to 12:10 |
Asymptotic completeness in nonrelativistic quantum field theory Chair: W.Craig
J.Derezinski |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
Regularity properties of the Melrose-Taylor Radon transform
A.Comech |
| 14:55 to 15:40 |
The explicit solution of the `D-bar'-Neumann problem in the non-isotropic siegel domain Chair: V.Ivrii
J.Tie |
| 15:40 to 16:20 |
Tea Break
|
| 16:30 to 17:15 |
Fourier analysis for vector-valued Sturm-Liouville problems
B.Levitan |
| 16:55 to 17:40 |
Pseudo-differential calculus on manifolds witha corners
B.-W.Schulze |
| 17:20 to 17:50 |
Tea Break
|
| 18:20 to 19:20 |
Fields Distinguished Lecture. I.
R.Melrose |
| 09:00 to 09:50 |
Microlocal analysis and CR-manifolds
C. Epstein |
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Local and global results for semilinear hyperbolic equations
D.Tataru |
| 11:20 to 12:10 |
A new type of estimate on Hilbert spaces Chair: P.Perry
N.Dencker |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
Scattering and regularity of the Schroedinger equation
W.Craig |
| 14:55 to 15:40 |
Upper bounds for the resonance counting function
R.Froese |
| 15:40 to 16:20 |
Tea Break
|
| 16:30 to 17:15 |
Scattering theory and deformations of asymptotically hyperbolic metrics Chair: E.Leichtnam
D.Borthwick |
| 16:55 to 17:40 |
Renormalization in quantum field theory on curved backgrounds as extension of distributions throug microlocal analysis
R.Brunetti |
| 17:00 to 17:55 |
On the Novikov conjecture on manifolds with boundary
P.Piazza |
| 18:00 to 18:55 |
Local solvability of some PDO's on the Heisenberg group
C.Winfield |
| 09:00 to 09:50 |
Progress in the use of layer potentials
M.Taylor |
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Nonlinear gluing via infinite dimensional Lagrangian intersections
R.Mazzeo |
| 11:20 to 12:10 |
Some inverse scattering problems Chair: J.Bruening
G.Eskin |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
About an index theorem for operators of Toeplitz type
E.Leichtnam |
| 14:55 to 15:40 |
Quasimodes associated to resonant elliptic periodic a trajectories Chair: M.Taylor
T.Paul |
| 15:40 to 16:10 |
Tea Break
|
| 16:00 to 16:45 |
Scattering matrix for scattering metrics
L.Parnovski |
| 16:55 to 17:50 |
Sharp bounds on the Green functions and heat kernel for symmetric spaces
L.Ji |
| 17:20 to 17:50 |
Tea Break
|
| 18:20 to 19:20 |
Fields Distinguished Lecture II
R.Melrose |
| 09:00 to 09:50 |
Second microlocal ellipticity and long timea existence for semilinear Klein-Gordon equation
J.-M.Delort |
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Microlocal energy estimates
N.Lerner |
| 11:20 to 12:10 |
Bounds on the eigenvalues of some partial differential operators Chair: J.Rauch
A.Laptev |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
Highly oscillatory multidimensional shocks
M.Williams |
| 14:55 to 15:40 |
Boundary value problems on manifolds with edges
E.Schrohe |
| 15:40 to 16:20 |
Tea Break
|
| 16:30 to 17:15 |
Scattering and Wigner measures Chair: Lizhen Ji
M.Rouleux |
| 17:20 to 18:05 |
Spectral asymptotics for compactly supported perturbations of the Laplacian on R^n
T.Christiansen |
| 18:00 to 18:55 |
Lower bounds on the number of resonances near the critical line
L.Farhy |
| 19:00 to 19:45 |
Resonances for Riemann surfaces
L. Guillope |
| 09:00 to 09:50 |
Microlocal analysis and inverse problems
G.Uhlmann |
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Scattering theory and locally symmetric manifolds of finite volume
W.Mueller |
| 11:20 to 12:10 |
The scattering operator and quasi-conformal deformations of Kleinian groups Chair: V.Guillemin
P.Perry |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
Holomorphic heat kernels and bounds for Hardya functions
J.Toth |
| 14:55 to 15:40 |
Global solution of an inverse problem for the acoustical wave equation Chair: A.Laptev
C.Nolan |
| 15:40 to 16:20 |
Tea Break
|
| 16:00 to 16:45 |
On some nonlinear problems of geometric origin
L.Kapitanski |
| 16:55 to 17:50 |
Pair correlations measures for spectral and scattering problems
S.Zelditch |
| 17:20 to 17:50 |
Tea Break
|
| 18:20 to 19:20 |
Fields Distinguished Lecture III
R.Melrose |
| 09:00 to 09:50 |
No Title Specified
|
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Singularities of the scattering amplitude for the Schroedinger equation with a long-range potential
D.Yafaev |
| 11:20 to 12:10 |
Propagation of singularities in three-body scattering Chair: G.Metivier
A.Vasy |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
Fourier integral operators with fold and cusp singularities
A.Greenleaf |
| 14:55 to 15:40 |
Propagation of growth and singularities for Schroedinger operators
J. Wunsch |
| 15:40 to 16:20 |
Tea Break
|
| 16:30 to 17:15 |
Regularity of degenerate Monge-Ampere equations Chair: V.Buslaev
P.Guan |
| 17:15 to 18:00 |
On estimating the number of negative eigenvalues of Schrodinger and other operators
G.Rozenblioum |
| 18:00 to 18:55 |
An inverse problem in elastodynamics
L.Rachele |
| 19:00 to 19:45 |
Applications of Hermite FIOs to dispersionless Toda and geometric quantization
A.Uribe |
| 09:00 to 09:50 |
Diffractive nonlinear geometric optics
J.Rauch |
| 09:50 to 10:20 |
Coffee Break
|
| 10:20 to 11:10 |
Global solutions to Maxwell equations in a ferromagnetic medium
G.Metivier |
| 11:20 to 12:10 |
Contribution of degenerate periodic orbits to the wave trace Chair: G.Popov
G.Popov |
| 12:10 to 14:00 |
Lunch
|
| 14:00 to 14:45 |
Pseudodifferential and analytic pseudodifferential operators on nilpotent groups
D.Geller |
| 14:55 to 15:40 |
Large eigenvalues and short geodesics on hyperbolic surfaces Chair: G.Uhlmann
C.Judge |
| 16:00 to 16:45 |
APS boundary conditions for manifolds with corners
G.Salomonsen |
| 16:55 to 17:50 |
Scattering transform and its inversion for the N-body Schroedinger equation at high energies
R.Novikov |
