
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR


WEYL
LAW at 100
a workshop
at the Fields Institute(map)
September 1921, 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 forwardlooking 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 nonselfadjoint 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 

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

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 nonselfadjoint 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 SophiaAntipolis)
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 NiceSophia Antipolis 
Lebeau, Gilles 
Université de Nice SophiaAntipolis 
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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