The Home Page of Maciej Zworski

Office: 801 Evans Hall
Fax:
(510) 6428204

Graduate Students
Postdoctoral Researchers
In Fall 2024 I am teaching Math 126, Introduction to PDE and Math 206, Functional Analysis.
In the Fall of 2004 and in the
Spring of 2011
I enjoyed two sabbatical semesters and
in 2017/2018 a sabbatical year.
In the Spring of 2023
I enjoyed another sabbatical semester.
Mathematical theory of
scattering resonances,
with Semyon Dyatlov.
Errata
The schedule of Bay Area Microlocal Analysis Seminar (BAMAS) can be found here.
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.
Pure and
Applied Analysis
Journal of Spectral Theory
Analysis & PDE
American Journal of Mathematics
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.
Internal waves in fluids and spectral theory of 0th order operators,
talks at Villa Finaly and
at University of Warsaw.
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.
My 19992008 papers can be found
here.
My more recent papers can be found below.

Overdamped QNM for Schwarzschild black holes (with Michael Hitrik), June 2024.

Discrete vs. continuous in the semiclassical limit,
(with Simon
Becker and Jens Wittsten), June 2024.

ClassicalQuantum correspondence in Lindblad evolution
(with Jeff Galkowski
and with an appendix joint with Zhen Huang),
June 2024.

Optimal enhanced dissipation for contact Anosov flows (with Zhongkai Tao),
October 2023.

Classically forbidden regions in the chiral model of twisted bilayer graphene (with Michael Hitrik and with an appendix joint with Zhongkai Tao),
October 2023.

Mathematical results on the chiral model of twisted bilayer graphene (with an appendix by
Mengxuan Yang and
Zhongkai Tao),
October 2023, to appear in J. Spectr. Theory.

From the chiral model of TBG to the BistritzerMacDonald model,
(with Simon
Becker), J. Math. Phys., 65 (2024), no. 6, Paper No. 062103, 13 pp.

An abstract formulation of the flat band condition
(with Jeff Galkowski),
July 2023, to appear in AMS Contemporary Mathematics volume in honor of Steve Zelditch.

Degenerate flat bands in twisted bilayer graphene,
(with
Simon Becker and Tristan Humbert), June 2023.

Dirac points for twisted bilayer graphene with inplane magnetic field,
(with Simon
Becker), J. Spectr. Theory, 14 (2024), no. 2, 479–511.

The scattering phase: seen at last,
(with Jeff Galkowski,
Pierre Marchand and
Jian Wang),
October 2022, SIAM Journal on Applied Matematics, 84(2024), 246–261.

Integrability in the chiral model of magic angles,
(with Simon Becker and Tristan Humbert), Comm. Math. Phys. 403(2023), 11531169.

Fine structure of flat bands in a chiral model of magic angles,
(with Simon Becker and Tristan Humbert), August 2022.

Mathematics of internal waves in a 2D aquarium,
(with Semyon Dyatlov and
Jian Wang), December 2021,
to appear in Analysis & PDE.

Viscosity limits for 0th order pseudodifferential operators,
(with Jeff Galkowski),
Communications on Pure and Applied Mathematics, 75(2022), 17981869.

An introduction to microlocal complex deformations,
(with Jeff Galkowski),
an expository companion to the paper above; December 2019.

Spectral characterization of magic angles in twisted bilayer graphene,
(with Simon Becker,
Mark Embree and
Jens Wittsten),
Physics Review B, 103, 165113, 2021.

Mathematics of magic angles in a model of twisted bilayer graphene,
(with Simon Becker,
Mark Embree and
Jens Wittsten),
Probability and Mathematical Physics,
3 (2022), no. 1, 69–103.

Honeycomb structures in magnetic fields,
(with Simon Becker,
Rui Han and
Svetlana Jitomirskaya), Journal of Physics A,
2021, vol.54, no.34, 345203.

Outgoing solutions via Gevrey2 properties, (with Jeff Galkowski), Annals of PDE (2021), no. 1, Paper No. 5, 13 pp.

Analytic hypoellipticity of Keldysh operators, (with Jeff Galkowski), Proceedings of the London Mathematical Society, (3)(2021), 119.

Fractal uncertainty for transfer operators
(with
Semyon Dyatlov),
International Mathematics Research Notices, 2020, no. 3, 781812.

Microlocal analysis of forced waves,
(with
Semyon Dyatlov),
Pure and Applied Analysis, 1(2019), 359394.

Magnetic oscillations in a model of graphene, (with Simon Becker),
Comm. Math. Phys.
367(2019), 941989.
An addendum to this paper clarifying an issue around BohrSommerfeld quantization conditions, July 2019.

Rough controls for Schrödinger operators on tori, (with Nicolas Burq), Annales Henri Lebesgue, 2 (2019), 331347.

Remarks on Vasy's operator with analytic coefficients
(with
Gilles Lebeau),
Proceedings of the AMS, 147(2019), 145152.

Commentary on ``Differentiable dynamical systems'' by Stephen Smale,
Bulletin of the AMS, 55 (2018), 331336.

A semiclassical approach to the KramersSmoluchowski equation
(with Laurent Michel),
SIAM Journal of Mathematical Analysis, 50(2018), 53625379.

Resonances for obstacles in hyperbolic space
(with Peter Hintz),
Comm. Math. Phys.
359(2018), 699731.
 Scattering resonances as viscosity limits,
in "Algebraic and Analytic Microlocal Analysis", M. Hitrik, D. Tamarkin, B. Tsygan, and S. Zelditch, eds. Springer, 2018.
A numerical illustration of the results and a MATLAB code
can be found here.

Wave decay for starshaped obstacles in R3: papers
of Morawetz and Ralston revisited,
(with Peter Hintz),
Mathematical Proceedings of the Royal Irish Academy,
117A (2017), 4762.

Mathematical study of scattering resonances,
Bulletin of Mathematical Sciences, 7(2017), 185.

Ruelle zeta function at zero for surfaces
(with
Semyon Dyatlov),
Inventiones mathematicae,
210(2017), 211229.
 A local trace formula for Anosov flows (with
Long Jin) with
an appendix by
Frédéric Naud,
Ann. Inst.
Henri Poincaré (A), 18(2017), 135.
I am grateful to Long Jin and Zhongkai Tao
for filling
a gap, and correcting a mistake, in the proof in a recent paper.
 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, Journal of Spectral Theory, 6(2016), 10871114.
A less formal account can be found here:

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. Erratum.

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.