The Home Page of Maciej Zworski
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Office: 897 Evans Hall
Fax:
(510) 642-8204
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In the Spring of 2012
I teach
Math 54: Linear Algebra and Differential Equations
Math 212: Several Complex Variables
In the Fall of 2004 and in the
Spring of 2011
I enjoyed my two sabbatical semesters.
The schedule of
The Paris
Nord-Berkeley 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),
Forges-les-eaux, 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 Evian-les-Bains, 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 Franco-Tunisien
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.
Theory and computation of resonances in 1d scattering:
David Bindel's website (still
in progress and developing) with his
easy-to-use MATLAB codes for computations of resonances.
Lecture notes: Version 0.95
for an advanced graduate course on ''Semiclassical Analysis'' (written with
L. C. Evans).
Lecture notes on resonances
preliminary version -- please beware.
My 1999-2008 papers can be found
here.
My more recent papers can be found below.
-
Weighted eigenfunction estimates with applications to compressed sensing
(with Nicolas Burq,
Semyon Dyatlov and
Rachel Ward),
November 2011.
-
Control for Schrödinger operators
on tori,
(with Nicolas Burq),
June 2011, to appear in Math. Res. Lett.
- Fractal Weyl law for open quantum chaotic maps (with
Stéphane Nonnenmacher
and Johannes
Sjöstrand), May 2011.
- From open quantum systems to open quantum
maps (with
Stéphane Nonnenmacher
and Johannes
Sjöstrand),
Comm. Math. Phys. 304(1)(2011), 1-48.
- Resolvent estimates for normally hyperbolic trapped sets (with
Jared Wunsch),
Ann. Inst. Henri Poincaré (A), 12(7)(2011), 1349-1385.
- 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), 363-425.
The 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), 305-334.
- Semiclassical resolvent estimates
in chaotic scattering
(with
Stéphane Nonnenmacher
),
Applied Mathematics Research
eXpress 2009; doi: 10.1093/amrx/abp003
- A mathematical formulation of the Mahaux-Weidenmüller 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), 1259-1301.
- Quantum decay rates in chaotic scattering
(with
Stéphane Nonnenmacher
),
Acta
Mathematica, Volume 203, Number 2/December, 2009, 149-233.