Papers and Preprints
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Weighted symbol spaces, magnetic translations, and pseudodifferential operators,
(with Reid Johnson), preprint, 2025.
pdf
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Weyl laws for exponentially small singular values of the d-bar operator,
(with Johannes Sjöstrand and
Martin Vogel), preprint, 2025.
pdf
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Overdamped QNM for Schwarzschild black holes,
(with Maciej Zworski), Annals of PDE, to appear.
pdf
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Classically forbidden regions in the chiral model of twisted bilayer graphene (with an appendix by
Zhongkai Tao and
Maciej Zworski)
(with Maciej Zworski), Probab. Math. Phys.,
6 (2025), 505-546. pdf
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A direct approach to the analytic Bergman projection,
(with Alix Deleporte and Johannes Sjöstrand), Ann. Fac. Sci. Toulouse Math., 33 (2024), 153-176.
pdf
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Characterizing boundedness of metaplectic Toeplitz operators,
(with Lewis Coburn and Johannes Sjöstrand), Int. Math. Res. Not., 10 (2024), 8264-8281.
pdf
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Complex FIOs and composition of Toeplitz operators,
(with Lewis Coburn and Johannes Sjöstrand), J. Pseudo-Differ. Oper. Appl., 14 (2023), 31 pp.
pdf
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Semiclassical Gevrey operators in the complex domain,
(with Richard Lascar, Johannes Sjöstrand, and Maher Zerzeri), Ann. Institut Fourier, 73 (2023), 1269-1318.
pdf
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Asymptotics for Bergman projections with smooth weights: a direct approach,
(with Matthew Stone), Analysis and Mathematical Physics, 12 (2022), 33 pp. pdf
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Adiabatic evolution and shape resonances,
(with Andrea Mantile and Johannes Sjöstrand), Memoirs of the AMS, 280 (2022), no. 1380, 102 pp.
pdf
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Semiclassical Gevrey operators on exponentially weighted spaces of holomorphic functions,
(with Richard Lascar, Johannes Sjöstrand, and Maher Zerzeri), Pure Appl. Funct. Analysis, 7 (2022), 641-653.
pdf
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Semiclassical Gevrey operators and magnetic translations,
(with Richard Lascar, Johannes Sjöstrand, and Maher Zerzeri), Journal of Spectral Theory, 12 (2022), 53-82.
pdf
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Weyl symbols and boundedness of Toeplitz opeators,
(with Lewis Coburn, Johannes Sjöstrand, and Francis White), Math. Res. Letters, 28 (2021), 681-696.
pdf
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Semigroup expansions for non-selfadjoint Schrödinger operators,
(with Ben Bellis), J. Functional Analysis, 277 (2019), 3586-3598.
pdf
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Positivity, complex FIOs, and Toeplitz operators,
(with Lewis Coburn and Johannes Sjöstrand), Pure and Applied Analysis, 1 (2019), 327-357.
pdf
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From semigroups to subelliptic estimates for quadratic operators,
(with Karel Pravda-Starov and Joe Viola), Trans. AMS. 370 (2018), 7391-7415.
pdf
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Two minicourses on analytic microlocal analysis,
(with Johannes Sjöstrand), "Algebraic and Analytic Microlocal Analysis", Springer Proceedings in Mathematics and Statistics, 269 (2018), 483-540. pdf
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Rational invariant tori and band edge spectra for non-selfadjoint operators,
(with Johannes Sjöstrand), J. Eur. Math. Soc. 20 (2018), 391-457..
pdf
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Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators,
(with Karel Pravda-Starov and Joe Viola), Bull. Sci. Math. 141 (2017), 615-675.
pdf
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Spectra for semiclassical operators with periodic bicharacteristics in dimension two,
(with Michael Hall and Johannes Sjöstrand), Int. Math. Res. Not. 20 (2015), 10243-10277.
pdf
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Tunnel effect and symmetries for non-selfadjoint operators, Journées "Équations aux Dérivées
Partielles'' (Biarritz, 2013), 10 pp., 2013. pdf
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Supersymmetric structures for second order differential operators,
(with Frédéric Hérau and Johannes Sjöstrand), Algebra i Analiz, 25 (2013), 125-154.
pdf
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Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators, (with
Emanuela Caliceti,
Sandro Graffi, and Johannes Sjöstrand), J. Phys. A: Math. Theor., 45 (2012), 444007.
pdf
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Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics, (with
Karel Pravda-Starov),
Ann. Institut Fourier, 63 (2013), 985-1032. pdf
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Resolvent estimates for elliptic quadratic differential operators,
(with Johannes Sjöstrand and Joe Viola), Analysis and PDE, 6 (2013), 181-196.
pdf
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Diophantine tori and Weyl asymptotics for non-selfadjoint operators in dimension two,
(with Johannes Sjöstrand), Comm. Math. Phys., 314 (2012), 373-417.
pdf
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Transmission eigenvalues for elliptic operators, (with Katya Krupchyk, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal., 43 (2011), 2630-2639.
pdf
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Tunnel effect and symmetries for Kramers-Fokker-Planck type operators,
(with Frédéric Hérau and Johannes Sjöstrand), Journal Inst. Math. Jussieu, 1 (2011), 567-634.
pdf
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The interior transmission problem and bounds on transmission eigenvalues, (with
Katya Krupchyk, Petri Ola, and Lassi Päivärinta), Math. Res. Lett. 18 (2011), no. 2, 279-293.
pdf
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Transmission eigenvalues for operators with constant coefficients,
(with Katya Krupchyk, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal. 42 (2010), no. 6, 2965-2986.
pdf
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Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics, (with
Karel Pravda-Starov),
Comm. Partial Differential Equations, 35 (2010), 988-1028.
pdf
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Spectra and Semigroup Smoothing for Non-elliptic Quadratic Operators, (with
Karel Pravda-Starov),
Math. Annalen, 344 (2009), 801-846.
pdf
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Tunnel Effect for Kramers-Fokker-Planck Operators: Return to Equilibrium and Applications,
(with Frédéric Hérau and Johannes Sjöstrand), Int. Math. Res. Not., 15 (2008), 48 pp.
pdf
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Rational Invariant Tori, Phase Space Tunneling, and Spectra for Non-Selfadjoint Operators in Dimension 2, (with
Johannes Sjöstrand),
Ann. Sc. Ecole Norm. Sup., 41(2008), 511-571.
pdf
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Tunnel Effect for Kramers--Fokker--Planck type Operators,
(with Frédéric Hérau and Johannes Sjöstrand), Ann. Henri Poincaré, 9 (2008), 209-274.
pdf
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Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions IIIa. One Branching Point, (with
Johannes Sjöstrand),
Can. J. Math., 60 (2008), 572-657.
pdf
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Diophantine Tori and Spectral Asymptotics for Non-Selfadjoint Operators,
(with Johannes Sjöstrand and San Vu Ngoc), Amer. J. Math., 129 (2007), 105-182.
pdf
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Energy Decay for Damped Wave Equations on Partially Rectangular Domains,
(with Nicolas Burq),
Math. Res. Letters, 14 (2007), 35-47. pdf
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Lagrangian Tori and Spectra for Non-Selfadjoint Operators (based on joint works with J. Sjöstrand and
S. Vu Ngoc), Séminaire Équations aux Dérivées Partielles, École Polytechnique, 14 pp., 2006.
pdf
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Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions II. Vanishing Averages, (with
Johannes Sjöstrand),
Comm. Partial Differential Equations, 30 (2005), 1065-1106.
pdf
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Boundary Spectral Behavior for Semiclassical Operators in Dimension One, Int. Math. Res. Not. 64 (2004), 3417-3438.
pdf
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Non-Selfadjoint Perturbations of Selfadjoint Operators in
2 Dimensions I, (with Johannes Sjöstrand), Ann. Henri Poincaré, 5 (2004), 1-73.
pdf
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Eigenfrequencies and Expansions for Damped Wave Equations, Meth. and Appl. of Analysis, 10 (2003), 543-564.
pdf
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Resolvent Expansions and Trace Regularizations for Schrödinger Operators,
(with Iosif Polterovich), Contemporary Mathematics, 327 (2003), 161-173.
pdf
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Regularized Traces and Taylor Expansions for the Heat
Semigroup, (with Iosif Polterovich), J. London Math. Soc. 68 (2003), 402-418. pdf
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Existence of Resonances in Magnetic Scattering, J.
Comp. Appl. Math. 148 (2002), 91-97. pdf
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Eigenfrequencies for Damped Wave Equations on Zoll
Manifolds, Asymptot. Analysis 31 (2002), 265-277.
pdf
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Expansions and Eigenfrequencies for Damped Wave Equations, Journées "Équations aux Dérivées
Partielles'' (Plestin-Les-Grèves, 2001), Exp. VI, 10 pp., 2001. pdf
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Properties of the Scattering Transform on the Real Line, J. Math. Anal. Appl. 258 (2001), 223-243.
pdf
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Stability of an Inverse Problem in Potential Scattering on
the Real Line, Comm. Partial Differential Equations
25 (2000), 925-955. pdf
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Bounds on Scattering Poles in One Dimension,
Comm. Math. Phys. 208 (1999), 381-411. pdf