Research

My main research interests are Berezin-Toeplitz operators, that one encounters when studying the semiclassical limit of geometric quantization, and classical and quantum integrable systems, in particular semitoric systems.

Articles and preprints

Disclaimer: the files available on this page may slightly differ from their published version. You may also find the list below on the French repository HAL. For more details about some of these works, see my habilitation thesis below.

Families of four-dimensional integrable systems with S^1-symmetries (avec Joseph Palmer). Preprint: arXiv:2307.10670. 125 pages.
Berezin-Toeplitz operators, Kodaira maps, and random sections (with Michele Ancona). To appear in American Journal of Mathematics. 31 pages.
The inverse spectral problem for quantum semitoric systems (with San Vũ Ngọc). Preprint: arXiv:2104.06704. 115 pages.
One can find a summary of this work in this entry of San Vũ Ngọc's blog.
Quantum propagation for Berezin-Toeplitz operators (with Laurent Charles). Preprint: arXiv:2009.05279. 43 pages.
Semitoric families (with Joseph Palmer). Memoirs of the American Mathematical Society, 1514, 2024. https://doi.org/10.1090/memo/1514 . 104 pages.
Correction to: Inverse spectral theory for semiclassical Jaynes-Cummings systems (with Álvaro Pelayo and San Vũ Ngọc). Mathematische Annalen, 375: 917-920, 2019. https://doi.org/10.1007/s00208-019-01868-7. 4 pages.
Bounds for fidelity of semiclassical Lagrangian states in Kähler quantization. Journal of Mathematical Physics, 59(8), 2018. https://doi.org/10.1063/1.5030410. 35 pages.
Symplectic geometry and spectral properties of classical and quantum coupled angular momenta (with Álvaro Pelayo). Journal of Nonlinear Science , 29(2): 655-708. https://doi.org/10.1007/s00332-018-9501-y. 54 pages.
Here is an animation of the joint spectrum when the parameter t varies; the red line is the boundary of the image of the momentum map, the critical value which transitions from elliptic-elliptic to focus-focus corresponds to the black circle, and blue dots are joint eigenvalues. Here R1 = 1, R2 = 5/2 and k = 5.
Spectral asymptotics of semiclassical unitary operators (with Álvaro Pelayo). Journal of Mathematical Analysis and Applications , 473(2):1174-1202, 2019. https://doi.org/10.1016/j.jmaa.2019.01.015. 29 pages.
Inverse spectral theory for semiclassical Jaynes-Cummings systems (with Álvaro Pelayo et San Vũ Ngọc). Mathematische Annalen, 364(3), 1393-1413, 2016. https://doi.org/10.1007/s00208-015-1259-z. 21 pages.
Unfortunately there is a small mistake in this paper, see the erratum listed above.
Euler Mac-Laurin formulas via differential operators (with Álvaro Pelayo). Advances in Applied Mathematics, 73:99-124, 2016. http://dx.doi.org/10.1016/j.aam.2015.10.001. 26 pages.
Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case. Analysis & PDE, 7(7):1595-1637, 2014. 43 pages.
Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: elliptic case. Communications in Partial Differential Equations, 39(2):213-243, 2014. 31 pages.

Books

A Brief Introduction to Berezin‐Toeplitz Operators on Compact Kähler Manifolds. CRM Short Courses, Springer International Publishing, 2018. ISBN: 978-3-319-94681-8. https://www.doi.org/10.1007/978-3-319-94682-5. Here is an erratum for this book; I would be grateful if you could communicate any additional mistake that you may encounter in the text.

Habilitation

Berezin-Toeplitz quantization and semitoric systems. Defended on November 17, 2023 at Université de Strasbourg.

Doctoral and postdoctoral supervision

PhD of Lucas Bourgoin, Geometry and asymptotics in quantum Hall states, co-supervision with Semyon Klevtsov, started October 2024.
Postdoc of Michele Ancona, 2021-2022.

Talks

Talks in conferences

Quantization in geometry, Cologne, Germany, July 2023.
Workshop on Finite dimensional integrability in mathematical physics, Les Diablerets, Switzerland, June 2023.
Journées de géométrie différentielle en mémoire de Pierre Molino, Saint-Mathieu de Tréviers, June 2022.
Rigidity, Inverse Problems and hyperbolic dynamics, Roscoff, March 2022.
Online Workshop on Integrability and Dynamics (online), Antwerp, Belgium, June 2021.
Semitoric systems and beyond, Antwerp, Belgium, September 2019.
Quantization in Symplectic Geometry, Cologne, Germany, July 2019.
Integrable Systems and Quantum Symmetries 25, Prague, Czechia, June 2017.
Spectral Theory and Mathematical Physics, Université de Lorraine, France, May 2017.
New trends in semiclassical analysis, Domaine de Chalès, France, December 2016.
Quantum mechanics meet symplectic topology, Tel Aviv University, Israel, May 2016.
Joint STAMP conference and 9th ICMAT International GMC Summer School on Symplectic Geometry, Classical Mechanics and Interactions with Spectral Theory, La Cristalera, Spain, July 2015.
Rencontre NOSEVOL 3, Université Rennes 1, April 2014.
AMS Special Session on Spectral, Index and Symplectic Geometry, Washington University in St. Louis, United States, October 2013.
Summer school Integrable Systems and Semiclassical Analysis, École Polytechnique Fédérale de Lausanne, Switzerland, July 2013.
Journées Louis Antoine, Université Rennes 1, October 2012.

Seminar talks

Séminaire Analyse Numérique et EDP, Institut de Mathématiques d'Orsay, France, November 2024.
Séminaire de géométrie, Institut Denis Poisson (Tours), France, March 2024.
UIUC symplectic and poisson geometry seminar (online), University of Illinois Urbana-Champaign, United States, April 2023.
Floris Takens seminar, University of Groningen, Netherlands, October 2022.
Geometry & Dynamics seminar (online), Tel Aviv University, Israel, October 2020.
Geometry & Dynamics seminar, Tel Aviv University, Israel, April 2019.
Séminaire EDP, IRMAR, Université Rennes 1, France, December 2018.
Analysis & Geometry Seminar, University of Antwerp, Belgium, December 2018.
Séminaire d'analyse fonctionnelle, Laboratoire Paul Painlevé, Université Lille 1, France, December 2016.
Symplectic Geometry Seminar, UC San Diego, United States, April 2016.
Séminaire d'analyse, LMJL, Université de Nantes, France, March 2016.
Séminaire de Physique Mathématique-EDP, Institut de Mathématiques de Bordeaux, France, March 2016.
Séminaire d'analyse, IRMA, Université de Strasbourg, France, December 2015.
Geometry & Topology seminar, University of Haifa, Israel, March 2015.
Geometry & Dynamics seminar, Tel Aviv University, Israel, December 2014.
Séminaire de physique mathématique, IMPA, Rio de Janeiro, Brazil, May 2012.

Student seminar talks

Working symplectic seminar, Tel Aviv University, Israel, February 2015.
Working symplectic seminar, Tel Aviv University, Israel, November 2014.
Séminaire Landau des jeunes chercheurs en analyse, Université Rennes 1, France, April 2014.
Séminaire Landau des jeunes chercheurs en analyse, Université Rennes 1, France, December 2012.

Working groups

2022: A probabilistic approach to Kähler-Einstein metrics, organized by Michele Ancona, Université de Strasbourg, France.
2021: The tight approximation property, organized by Michele Ancona, Université de Strasbourg, France.
2017-2018: Uncertainty principles organized by Alix Deleporte, Université de Strasbourg, France.
2016-2017: GDT Stein, organized by Emmanuel Opshtein, Université de Strasbourg, France: the goal was to understand (part of) the book From Stein to Weinstein and Back. Symplectic Geometry of Affine Complex Manifolds by K. Cieliebak and Y. Eliashberg.
2014-2016: Working symplectic seminar, Tel Aviv University, Israel: working group for postdoc students in symplectic geometry at TAU.

PhD thesis

Théorie spectrale inverse pour les opérateurs de Toeplitz 1D. Supervised by San Vũ Ngọc and Laurent Charles and defended on June 19, 2014 at Université Rennes 1.

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