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THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR
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WEYL
LAW at 100
a workshop
at the Fields Institute(map)
September 19-21, 2012
Organizer: Maciej Zworski, UC Berkeley
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Supported by NSF award #: 1216660 |
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In 1912 Hermann Weyl published his paper establishing the Weyl
law which gives the leading asymptotic description for the counting
function of eigenvalues of the Dirichlet or Neumann Laplacian on
a bounded domain in the Euclidean space. He later conjectured the
form of the second term in asymptotics of the counting functions.
After contributions by many mathematicians, among them, Courant,
Hilbert, Avakumovic, Levitan, Hörmander, Seeley, Duistermaat,
Guillemin, Melrose and Sjöstrand, the Weyl conjecture was solved
by Ivrii in 1982. The workshop is intended as forward-looking celebrations
of the 100th anniversary of Weyl's paper, and of Victor Ivrii's
contributions to the subject.
Some of topics presented in the workshops are: Weyl laws for perturbations
of non-selfadjoint operators, connections to random matrix theory
and to the metropolis algorithm, spectral problems for fractional
powers of the Laplacian, fractal Weyl laws for resonances of classically
chaotic systems, eigenvalue/resonance measurement in scanning tunneling
microscopy and in microwave billiards, numerical methods for resonance
calculations.
SPEAKERS:
Ivana Alexandrova, SUNY
Albany
David Bindel, Cornell University
Semyon Dyatlov, UC Berkeley
Rupert Frank, Princeton University
Michael Hitrik, UCLA
Dimitry Jakobson, McGill
University
Ulrich Kuhl, Université
de Nice
Gilles Lebeau, Université
de Nice
Richard Melrose, MIT
Hari Manoharan, Stanford
University
Yuri Safarov, King's College,
London
Chris Sogge, The Johns Hopkins
University
Melissa Tacy, Northwestern University
Daniel Tataru, UC Berkeley
John Toth, McGill Universtiy
Andras Vasy, Stanford University
Steve Zelditch, Northwestern
University
PUBLIC
LECTURE
Thursday, September 20, 4 PM
Stéphane
Nonnenmacher, Commissariat
à l'énergie atomique, Saclay
Counting stationary modes: a discrete view of geometry
and dynamics |
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Schedule
| Wednesday September 19, 2012 |
| 8:30 - 9:00 |
Onsite Registration Morning
Coffee |
| 9:00 -10:00 |
Richard Melrose (MIT)
Eigenvalues, transmission and transition |
| 10:00 - 10:15 |
Break |
| 10:15 -11:15 |
Daniel Tataru (UC Berkeley) (presentation)
Sharp Lp bounds on spectral clusters for rough metrics |
| 11:15 - 12:15 |
Rupert Frank (Princeton University) (presentation)
A microscopic derivation of Ginzburg- Landau theory
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| 12:15 - 1:45 |
Lunch |
| 1:45 - 2:45 |
Dmitry Jakobson (McGill)
Nodal sets and negative eigenvalues in conformal geometry |
| 2:45 - 3:00 |
Break |
| 3:00 - 4:00 |
Michael Hitrik (UCLA)
Tunnel effect and symmetries for non-self-adjoint operators
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| 4:00 - 5:00 |
Melissa Tacy (Northwestern University)
(presentation)
Directional Localization and Toral Eigenfunctions |
| Thursday September 20, 2012 |
| 8:30 - 9:00 |
Morning Coffee |
| 9:00 - 10:00 |
Gilles Lebeau (Université
de Nice) (presentation)
Hypoelliptic random walks |
| 10:00 - 10:15 |
Break |
| 10:15 - 11:15 |
Hari Manoharan (Stanford University)
A Tale of Two Spectra: Quantum Drums Beat as One |
| 11:15 - 12:15 |
Ulrich Kuhl ( Université de Nice Sophia-Antipolis)
Weyl asymptotics in microwave experiments: From closed
to open system
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| 12:15 - 1:45 |
Lunch |
| 1:45 - 2:45 |
David Bindel (Department of
Computer Science, Cornell University)
Numerical Analysis of Resonances |
| 2:45 - 3:45 |
Semyon Dyatlov (University
of California, Berkeley)
Fractal Weyl laws for resonances |
| 3:45 - 4:00 |
Coffee Break |
| 4:00 - 5:00 |
Public
Lecture
Stéphane Nonnenmacher
(Commissariat à l'énergie atomique, Saclay)
Counting stationary modes: a discrete view of geometry and
dynamics |
| 5:00 - 7:00 |
Reception |
| Friday September 21, 2012 |
| 8:30 - 9:00 |
Morning Coffee |
| 9:00 - 10:00 |
Chris Sogge (Johns Hopkins University}(presentation)
A couple of endpoint restriction theorems for eigenfunctions
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| 10:00 - 10:15 |
Break |
| 10:15 - 11:15 |
John Toth (McGill Universtiy) (presentation)
(presentation)
Intersection Bounds for Nodal Sets of Planar Neumann Eigenfunctions
with Interior Analytic Curves
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| 11:15 - 12:15 |
András Vasy (Stanford University)
The Laplacian on differential forms on asymptotically hyperbolic
spaces
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| 12:15 - 1:45 |
Lunch |
| 1:45 - 2:45 |
Yuri Safarov (King's College, London)
Ergodicity of branching billiards |
| 3:00 - 3:45 |
Ivana Alexandrova (SUNY Albany)
Resonances in Scattering by Two Magnetic Fields at Large
Separation |
| 3:45 - 4:00 |
Coffee Break |
| 4:00 - 5:00 |
Steve Zelditch (Northwestern University)
(presentation)
Ergodicity and intersections of nodal sets and geodesics
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List of Participants (as of September 17, 2012)
| Full Name |
University/Affiliation |
| Alexandrova, Ivana |
SUNY Albany |
| Bindel, David |
Cornell University |
| Canzani, Yaiza |
McGill University |
| Datchev, Kiril |
Massachusetts Institute of Technology |
| Dyatlov, Semyon |
University of California, Berkeley |
| Eswarathasan, Suresh |
McGill University |
| Frank, Rupert |
Princeton University |
| Galkowski, Jeffrey |
University of California, Berkeley |
| Gannot, Oran |
University of California, Berkeley |
| Haber, Nick |
Stanford University |
| Hitrik, Michael |
University of California, Los Angeles |
| Jakobson, Dmitry |
McGill University |
| Kang, Daniel |
Massachusetts Institute of Technology |
| Kessler, Andre |
Massachusetts Institute of Technology |
| Kuhl, Ulrich |
Université de Nice-Sophia Antipolis |
| Lebeau, Gilles |
Université de Nice Sophia-Antipolis |
| Manoharan, Hari |
Stanford University |
| Melrose, Richard |
Massachusetts Institute of Technology |
| Nonnenmacher, Stéphane |
CEA Saclay |
| Safarov, Yuri |
King's College |
| Sogge, Christopher |
Johns Hopkins University |
| Tacy, Melissa |
Northwestern University |
| Tataru, Daniel |
University of California, Berkeley |
| Toth, John |
McGill University |
| Vasy, András |
Stanford University |
| Ventura, Ivan |
University of Arizona |
| Zelditch, Steve |
Northwestern University |
| Zhu, Xuwen |
Massachusetts Institute of Technology |
| Zworski, Maciej |
University of California, Berkeley |
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