April 24, 2014
WEYL LAW at 100
a workshop
at the Fields Institute
September 19-21, 2012

Organizer: Maciej Zworski, UC Berkeley

Supported by NSF award #: 1216660

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.


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

Thursday, September 20, 4 PM
Stéphane Nonnenmacher, Commissariat à l'énergie atomique, Saclay
Counting stationary modes: a discrete view of geometry and dynamics


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

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
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

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

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

11:15 - 12:15

András Vasy (Stanford University)
The Laplacian on differential forms on asymptotically hyperbolic spaces

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

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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