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 and gauge theories.

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 thesis (2018) can be found here.


List of publications and preprints

  1. An index theorem on asymptotically static spacetimes with compact Cauchy surface (with Dawei Shen), arXiv:2104.02816 (40 p.), 2021
  2. Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces (with Nguyen Viet Dang), arXiv:2012.00712 (88 p.), 2020
  3. The Unruh state for massless fermions on Kerr spacetime and its Hadamard property (with Christian Gérard and Dietrich Häfner), accepted in Annales Scientifiques de l'École Normale Supérieure, arXiv:2008.10995 (61 p.), 2020
  4. 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, 10.1017/S147474802000002X, arXiv:1812.06564, (2020)
  5. Wick rotation of the time variables for two-point functions on analytic backgrounds, Letters in Mathematical Physics, 110, 585–609, arXiv:1808.03859, (2020)
  6. 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)
  7. The massive Feynman propagator on asymptotically Minkowski spacetimes II (with Christian Gérard), International Mathematics Research Notices 20, 6856–6870, arXiv:1806.05076, (2020)
  8. Conformal extension of the Bunch-Davies state across the de Sitter boundary, Journal of Mathematical Physics 60 (2), 022301, arXiv:1711.04011, (2019)
  9. 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)
  10. The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes, Letters in Mathematical Physics 107 (12), 2291–2331, arXiv:1612.01203, (2017)
  11. The massive Feynman propagator on asymptotically Minkowski spacetimes (with Christian Gérard), American Journal of Mathematics 141 (6), 1501–1546, arXiv:1609.00192, (2019)
  12. 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)
  13. 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)
  14. 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)
  15. Construction of Hadamard states by characteristic Cauchy problem (with Christian Gérard), Analysis & PDE, 9 (1), 111–149, arXiv:1409.6691, (2016)
  16. 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)
  17. 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)
  18. Continuous and holomorphic functions with values in closed operators (with Jan Dereziński), Journal of Mathematical Physics 55 (8), 083512, arXiv:1309.0164, (2013)
  19. On–shell extension of distributions (with Dorothea Bahns), Annales Henri Poincaré, 15 (10), 2045–2067, arXiv:1260.5448, (2014)
  20. Construction of Hadamard states by pseudo–differential calculus (with Christian Gérard), Communications in Mathematical Physics, 325 (2), 713–755, arXiv:1209.2604, (2013)
  21. Quantum Field Theory in static external potentials and Hadamard states, Annales Henri Poincaré, 13 (8), 1841–1871, arXiv:1108.2982, (2012)
  22. Exactly solvable Schrödinger operators (with Jan Dereziński), Annales Henri Poincaré, 12 (2), 397–418, arXiv:1009.0541 (2011)

Proceedings

  1. The Feynman problem for the Klein-Gordon equation (with Christian Gérard), Séminaire Laurent Schwartz — EDP et applications, arXiv:2003.14404, (2020)

Some slides