The Home Page of Maciej Zworski

Office: 801 Evans Hall
Fax:
(510) 6428204

In the Fall of 2015 I was a Miller Research Professor
In the Spring of 2016 I am teaching Several Complex Variables.
Graduate Students
Postdoctoral Researchers
In the Fall of 2004 and in the
Spring of 2011
I enjoyed my two sabbatical semesters.
''Semiclassical Analysis''
Graduate Studies in Mathematics 138, AMS
Errata
The schedule of
The Paris/Berkeley/Bonn/Zurich Analysis Seminar can be found here.
Information about journals with which I am affiliated can be found below.
Analysis & PDE
American Journal of Mathematics
Applied Mathematics Research eXpress
Methods and Applications
of Analysis
I study mathematical aspects of
quantum mechanics, more specifically
scattering theory and microlocal analysis. CV.
Some recent talks:
Fractal Weyl laws in chaotic scattering ,
RES04, January 2004.
Control theory and high energy eigenfunctions,
(with Nicolas Burq),
Forgesleseaux, June 2004. Here is the short note for the
proceedings.
Fractal Weyl laws for open quantum maps ,
SCATT05, March 2005.
Quantum decay rates in chaotic scattering ,
Talk at Ecole Polytechnique, May 2006.
Soliton scattering by delta impurities ,
Colloque EDP EvianlesBains, June 2006.
What are the residues of resolvents of Laplacians on
symmetric spaces? ,
Summers School: Microlocal
and Geometric Methods in Representation Theory, July 2006.
Quantum decay rates in chaotic scattering
(with Stéphane Nonnenmacher),
AMS National Meeting,
New Orleans, January 2007.
Quantum chaos in scattering theory
Colloquium talks 2006/08 at
First Joint CMS/SMM Meeting
, Northwestern, Univ. of North Carolina, and Univ. of Washington.
Soliton Home Movies, a popular talk for
prospective graduate students (a reasonably decent PDF viewer might be
needed to see the movies)
A minicourse at The Summer Graduate Worskhop on Inverse Problems, July 2009:
I, II, III, IV, V.
Two solitons in an external field,
Colloque FrancoTunisien
d'EDP, Hammamet, 2009.
Mathematics of quantum resonances,
The Joint BMC/BAMC Meeting of 2010.
Semiclassical scattering and applications,
Colloquium, Stanford, January 2011.
Solitons in external fields,
Séminaire EDP, Ecole Polytechnique/IHES, February 2011.
From classical to quantum and back,
Colloquium at Banach Center
Warsaw and at Purdue University.
Linear vs chaotic, talk at
2016 Breakthrough Prize Symposium: A Multilingual Conversation in Science.
Theory and computation of resonances in 1d scattering:
David Bindel's website (still
in progress and developing) with his
easytouse MATLAB codes for computations of resonances.
Mathematical theory of
scattering resonances, version 0.03,
book in progress with
Semyon Dyatlov.
My 19992008 papers can be found
here.
My more recent papers can be found below.

Mathematical study of scattering resonances, a survey,
August 2016.

Remarks on Vasy's operator with analytic coefficients
(with
Gilles Lebeau),
August 2016.

Ruelle zeta function at zero for sufaces
(with
Semyon Dyatlov),
June 2016.
 A Fermi golden rule for quantum graphs
(with
Minjae Lee),
Journal of Mathematical Physics, 57, 092101 (2016).
 Resonances for asymptotically hyperbolic manifolds:
Vasy's method revisited, November 2015,
to appear in Journal of Spectral Theory.
A less formal account can be found here:
 Scattering resonances as viscosity limits,
April 2015, to appear in
in "Algebraic and Analytic Microlocal Analysis", M. Hitrik, D. Tamarkin, B. Tsygan, and S. Zelditch, eds. Springer.
A numerical illustration of the results and a MATLAB code
can be found here.
 A local trace formula for Anosov flows (with
Long Jin) with
an appendix by
Frédéric Naud, November 2014, to appear in
Ann. Inst.
Henri Poincaré (A)

Dynamical zeta function for Anosov flows via microlocal
analysis
(with
Semyon Dyatlov),
Annales de l'ENS,
49(2016), 543577.

Heat traces and existence of scattering resonances for bounded potentials
(with
Hart F. Smith),
Annales de l'Institut Fourier,
66 (2016), 455475.

Stochastic stability of PollicottRuelle resonances
(with
Semyon Dyatlov),
Nonlinearity,
28(2015), 35113534.

Resonances and lower resolvent bounds
(with
Kiril Datchev and
Semyon Dyatlov),
Journal of Spectral Theory, 5(2015), 599615.
 Decay of correlations for normally hyperbolic trapping, (with
Stéphane Nonnenmacher),
Inventiones mathematicae,
200(2)(2015), 345438.
 Fractal Weyl law for open quantum chaotic maps (with
Stéphane Nonnenmacher
and Johannes
Sjöstrand),
Annals of Math. 179(1)(2014), 179251.

Sharp polynomial bounds on the number of PollicottRuelle resonances
(with
Kiril Datchev and
Semyon Dyatlov),
Ergodic Theory and Dynamical Systems,
34(4)(2014), 11681183.

Trapping of waves and null geodesics for rotating black holes
(with
Semyon Dyatlov),
Phys. Rev. D 88, 084037 (2013)

Control for Schrödinger operators
on 2tori: rough potentials,
(with Jean Bourgain, and Nicolas Burq), Journal of the European Mathematical Society, 15(2013), no.5, 15971628.

Experimental observation of spectral gap in microwave ndisk systems
(with Sonya Barkhofen, Tobias Weich,
Alexander Potzuweit, Ulrich Kuhl and H.J. Stöckmann), Phys. Rev. Lett.
110, 164102 (2013).

Pointwise bounds on quasimodes of semiclassical Schrödinger
operators in dimension two
(with
Hart F. Smith),
Math. Res. Lett.
20(2013), 401408.

Weyl asymptotics: from closed to open systems
(with
Alexander Potzuweit, Tobias Weich, Sonya Barkhofen, Ulrich Kuhl and H.J. Stöckmann),
Phys. Rev. E. 86, 066205 (2012).

A quantitative version
of CatlinD'AngeloQuillen theorem
(with
Alexis Drouot),
Analysis and Mathematical Physics, 3(2013), no.1, 119.

Quantum ergodicity
for restrictions to hypersurfaces
(with
Semyon Dyatlov), Nonlinearity, 26(2013), 3552.

Weighted eigenfunction estimates with applications to compressed sensing
(with Nicolas Burq,
Semyon Dyatlov and
Rachel Ward),
SIAM J. Math. Anal., 44(5)(2012), 34813501.

Control for Schrödinger operators
on tori,
(with Nicolas Burq),
Math. Res. Lett. 19(2)(2012), 309324.
 From open quantum systems to open quantum
maps (with
Stéphane Nonnenmacher
and Johannes
Sjöstrand),
Comm. Math. Phys. 304(1)(2011), 148.
 Resolvent estimates for normally hyperbolic trapped sets (with
Jared Wunsch),
Ann. Inst. Henri Poincaré (A), 12(7)(2011), 13491385.
 Effective dynamics of double solitons for perturbed mKdV(with
Justin Holmer and
Galina Perelman), with an appendix by Bernd Sturmfels, Comm. Math. Phys. 305(3)(2011), 363425.
Numerical illustrations of the results and MATLAB codes
can be found here. Related numerical
results can be found in a
paper
by Trevor Potter.
 Probabilistic Weyl laws for quantized tori(with
Tanya J. Christiansen),
Comm. Math. Phys. 299(2)(2010), 305334.
 Semiclassical resolvent estimates
in chaotic scattering
(with
Stéphane Nonnenmacher
),
Applied Mathematics Research
eXpress 2009; doi: 10.1093/amrx/abp003
 A mathematical formulation of the MahauxWeidenmüller formula for the scattering matrix(with
Tanya J. Christiansen),
J. Phys. A: Math. Theor., 42 (2009) 415202.
 Breathing patterns in nonlinear relaxation(with
Justin Holmer),
Nonlinearity,
22(2009), 12591301.
 Quantum decay rates in chaotic scattering
(with
Stéphane Nonnenmacher
),
Acta
Mathematica, Volume 203, Number 2/December, 2009, 149233.