Research interests

My principal area of research is mathematical physics and I am particularly interested in applications of methods from partial differential equations, microlocal or asymptotic analysis and spectral theory, often in geometric contexts.

Presently my main research topic is Quantum Field Theory on curved spacetimes, and I have worked on problems including Hadamard states, renormalisation, AdS/CFT correspondence, QFT in external potentials, gauge theories and index theory.

More generally, I am interested in various problems where there is a relationship between classical and quantum dynamics, or where local and global aspects are tied together in an intricate way.

My habilitation (2018, in French) can be found here.

Research group

Current PhD students

  • Ashkan Sadat Kyaee (Utrecht), MSc Sorbonne Université
  • Ruben Zeitoun (Cergy Paris), MSc ENS Lyon

Current postdocs

  • Nicolas Frantz (Cergy Paris), PhD Université de Lorraine, Metz
  • Christiane Klein (Cergy Paris / Grenoble, with Dietrich Häfner), PhD Universität Leipzig

List of publications and preprints

  1. IR-fixed Euclidean vacuum for linearized gravity on de Sitter space (with Christian Gérard), arXiv:2405.00866 (56 p.), 2024
  2. Reconstruction of a Lorentzian manifold from its Dirichlet-to-Neumann map (with Alberto Enciso and Gunther Uhlmann), arXiv:2303.08430 (21 p.), 2023
  3. Wick rotation of linearized gravity in Gaussian time and Calderón projectors (with Christian Gérard and Simone Murro), arXiv:2204.01094 (63 p.), 2023
  4. Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces (with Nguyen Viet Dang), Journal of the European Mathematical Society (JEMS), 10.4171/JEMS/1389, arXiv:2012.00712, (2023)
  5. The Unruh state for massless fermions on Kerr spacetime and its Hadamard property (with Christian Gérard and Dietrich Häfner), Annales Scientifiques de l'École Normale Supérieure, 1 (56), 127–196, arXiv:2008.10995, (2023)
  6. The wave resolvent for compactly supported perturbations of static spacetimes (with Ruben Zeitoun), in: M. Ruzhansky et al. (eds), Harmonic Analysis and Partial Differential Equations, Trends in Mathematics, Springer, arXiv:2204.01094, (2022)
  7. Dynamical residues of Lorentzian spectral zeta functions (with Nguyen Viet Dang), Journal de l'École polytechnique — Mathématiques, 9, 1245–1292, arXiv:2108.07529, (2022)
  8. An index theorem on asymptotically static spacetimes with compact Cauchy surface (with Dawei Shen), Pure and Applied Analysis, 4 (4), 727–766, arXiv:2104.02816, (2022)
  9. Propagation of singularities on AdS spacetimes for general boundary conditions and the holographic Hadamard condition (with Oran Gannot), Journal of the Institute of Mathematics of Jussieu  21 (1), 67–127, arXiv:1812.06564, (2022)
  10. Wick rotation of the time variables for two-point functions on analytic backgrounds, Letters in Mathematical Physics, 110, 585–609, arXiv:1808.03859, (2020)
  11. The massive Feynman propagator on asymptotically Minkowski spacetimes II (with Christian Gérard), International Mathematics Research Notices  20, 6856–6870, arXiv:1806.05076, (2020)
  12. A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes (with Wojciech Dybalski), Classical and Quantum Gravity  36 (8), arXiv:1809.05123, (2019)
  13. Conformal extension of the Bunch-Davies state across the de Sitter boundary, Journal of Mathematical Physics  60 (2), 022301, arXiv:1711.04011, (2019)
  14. The massive Feynman propagator on asymptotically Minkowski spacetimes (with Christian Gérard), American Journal of Mathematics  141 (6), 1501–1546, arXiv:1609.00192, (2019)
  15. Analytic Hadamard states, Calderón projectors and Wick rotation near analytic Cauchy surfaces (with Christian Gérard), Communications in Mathematical Physics  366 (1), arXiv:1609.00192, (2019)
  16. Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes (with András Vasy), Annales Henri Poincaré  19 (5), 1529–1586, arXiv:1512.08052, (2018)
  17. The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes, Letters in Mathematical Physics  107 (12), 2291–2331, arXiv:1612.01203, (2017)
  18. Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry (with Christian Gérard and Omar Oulghazi), Communications in Mathematical Physics  352 (2), 519-583, arXiv:1602.00930, (2017)
  19. Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime (with Jochen Zahn), Reviews in Mathematical Physics  29 (4), 1750014, arXiv:1407.8079, (2017)
  20. Construction of Hadamard states by characteristic Cauchy problem (with Christian Gérard), Analysis & PDE  9 (1), 111–149, arXiv:1409.6691, (2016)
  21. Hadamard property of the in and out states for Klein-Gordon fields on asymptotically static spacetimes (with Christian Gérard), Annales Henri Poincaré  18 (8), 2715–2756, arXiv:1609.00190, (2016)
  22. Hadamard states for the linearized Yang-Mills equation on curved spacetime (with Christian Gérard), Communications in Mathematical Physics   337 (1), 253–320, arXiv:1403.7153, (2015)
  23. On–shell extension of distributions (with Dorothea Bahns), Annales Henri Poincaré, 15 (10), 2045–2067, arXiv:1260.5448, (2014)
  24. Continuous and holomorphic functions with values in closed operators (with Jan Dereziński), Journal of Mathematical Physics  55 (8), 083512, arXiv:1309.0164, (2013)
  25. Construction of Hadamard states by pseudo–differential calculus (with Christian Gérard), Communications in Mathematical Physics  325 (2), 713–755, arXiv:1209.2604, (2013)
  26. Quantum Field Theory in static external potentials and Hadamard states, Annales Henri Poincaré  13 (8), 1841–1871, arXiv:1108.2982, (2012)
  27. Exactly solvable Schrödinger operators (with Jan Dereziński), Annales Henri Poincaré  12 (2), 397–418, arXiv:1009.0541, (2011)

Proceedings

  1. Lorentzian spectral zeta functions on asymptotically Minkowski spacetimes (with Nguyen Viet Dang), to appear in: A. Galstyan et al. (eds), Analysis, Applications, and Computations - Selected contributions of the 13th ISAAC Congress, Ghent, Belgium, 2021, arXiv:2202.06408, (2022)
  2. The Feynman problem for the Klein-Gordon equation (with Christian Gérard), Séminaire Laurent Schwartz — EDP et applications (2019-2020), Exposé no. 4, arXiv:2003.14404, (2022)

Some slides


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