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.

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

- Nicolas Frantz (Cergy Paris), PhD Université de Lorraine, Metz

- Christiane Klein (Cergy Paris / Grenoble, with Dietrich Häfner), PhD Universität Leipzig

- IR-fixed Euclidean vacuum for linearized gravity on de Sitter space (with Christian Gérard), arXiv:2405.00866 (56 p.), 2024
- Reconstruction of a Lorentzian manifold from its Dirichlet-to-Neumann map (with Alberto Enciso and Gunther Uhlmann), arXiv:2303.08430 (21 p.), 2023
- Wick rotation of linearized gravity in Gaussian time and Calderón projectors (with Christian Gérard and Simone Murro), arXiv:2204.01094 (63 p.), 2023
- 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) - 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) - 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) - Dynamical
residues of Lorentzian spectral zeta functions
(with Nguyen Viet Dang),
*Journal de l'École polytechnique — Mathématiques*, 9, 1245–1292, arXiv:2108.07529, (2022) - 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) - 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) - Wick
rotation of the time variables for two-point functions on
analytic backgrounds,
*Letters in Mathematical Physics*, 110, 585–609, arXiv:1808.03859, (2020) - The
massive Feynman propagator on asymptotically Minkowski
spacetimes II (with Christian Gérard),
*International Mathematics Research Notices*20, 6856–6870, arXiv:1806.05076, (2020) - 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) - Conformal
extension of the Bunch-Davies state across the de Sitter
boundary,
*Journal of Mathematical Physics*60 (2), 022301, arXiv:1711.04011, (2019) - The
massive Feynman propagator on asymptotically Minkowski
spacetimes (with Christian Gérard),
*American Journal of Mathematics*141 (6), 1501–1546, arXiv:1609.00192, (2019) - 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)
- 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)
- The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes, Letters in Mathematical Physics 107 (12), 2291–2331, arXiv:1612.01203, (2017)
- 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)
- 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)
- Construction of Hadamard states by characteristic Cauchy problem (with Christian Gérard), Analysis & PDE 9 (1), 111–149, arXiv:1409.6691, (2016)
- 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) - 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)
- On–shell extension of distributions (with Dorothea Bahns), Annales Henri Poincaré, 15 (10), 2045–2067, arXiv:1260.5448, (2014)
- Continuous and holomorphic functions with values in closed operators (with Jan Dereziński), Journal of Mathematical Physics 55 (8), 083512, arXiv:1309.0164, (2013)
- Construction of Hadamard states by pseudo–differential calculus (with Christian Gérard), Communications in Mathematical Physics 325 (2), 713–755, arXiv:1209.2604, (2013)
- Quantum Field Theory in static external potentials and Hadamard states, Annales Henri Poincaré 13 (8), 1841–1871, arXiv:1108.2982, (2012)
- Exactly solvable Schrödinger operators (with Jan Dereziński), Annales Henri Poincaré 12 (2), 397–418, arXiv:1009.0541, (2011)

- 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) - 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)

- An invitation to Quantum Field Theory on curved spacetimes, MSRI Berkeley, 2019
- Champs de Klein-Gordon au bord conforme d'espaces-temps, Cergy-Pontoise, 2020