Professor

Junior member of the Institut Universitaire de France (2020-2025)

• Research topics: semiclassical analysis, dynamical systems, mathematical physics.
  
• Research articles: (the published version may slightly differ from the preprint version)

1. Entropy of semiclassical measures in dimension 2 (preprint, Duke Math. J., Vol. 155, N° 2 (2010), 271-335, see here).
2. Entropy of semiclassical measures for nonpositively curved surfaces (preprint, Annales Henri Poincaré, Vol. 11, N°6 (2010), 1085-1116, AHP Distinguished Paper, see here).
3. Entropy of semiclassical measures for symplectic linear maps of the multidimensional torus (preprint, Int. Math. Res. Notices, Vol. 2011, N°11 (2011), 2396-2443 see here).
4. Dispersion and controllability for the Schrödinger equation on negatively curved manifolds , with N. Anantharaman (preprint, Analysis & PDE, Vol. 5, N°2 (2012), 313-338 see here).
5. Delocalization of slowly damped eigenmodes on Anosov manifolds , (preprint, Comm. in Math. Phys., Vol. 316, N°2 (2012), 555-593 see here).
6. Eigenmodes of the damped wave equation and small hyperbolic subsets, with an appendix in collaboration with S. Nonnenmacher (preprint, Annales de l'Institut Fourier, Vol.  64 , N°3 (2014), 1229-1267, see here).
7. Remarks on quantum ergodicity, (preprint, Journal of Modern Dynamics, Vol. 7, N°1 (2013), 119-133 see here).
8. Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces, with S. Eswarathasan (preprint, J. Inst. Math. Jussieu, Vol. 16, N°4 (2017), 787-835, see here)
   
9. Lp norms, nodals sets, and quantum ergodicity, with H. Hezari (preprint, Adv. Math., Vol. 290 (2016), 938-966, see here)
10. Long-time dynamics of the perturbed Schrödinger equation on negatively curved surfaces, (preprint, Ann. H. Poincaré, Vol. 17, N°8 (2016), 1955-1999, see here)
11. Quantitative equidistribution properties of toral eigenfunctions, with H. Hezari  (preprint, J. Spectral Theory, Vol. 7 (2017), 471-485, see here)
    
12. Concentration and non concentration for the Schrödinger evolution on Zoll manifolds, with F. Macià (preprint, Comm. Math. Physics, Vol. 345, N°3 (2016), 1019-1054, see here)
13. Equidistribution of the conormal cycle of random nodal sets, with N.V. Dang (preprint, J. Eur. Math. Soc., Vol. 20, N°12 (2018), 3017-3071, see here) 
14. Spectral analysis of Morse-Smale gradient flows, with N.V. Dang (preprint,
    Ann. Sci. ENS, Vol. 52 (2019), 1403-1458, see here)
15. Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces, with N.V. Dang (preprint, J. Inst. Math. Jussieu, Vol. 19 (2020), 1409-1465, see here)
16. Spectral analysis of Morse-Smale flows II: resonances and resonant states, with N.V. Dang (preprint, American J. Math., Vol. 142 (2020), 547-593, see here)
    
17. Topology of Pollicott-Ruelle resonant states, with N.V. Dang (preprint),
    Ann. Sc. Norm. Sup. di Pisa, Vol. XXI, (2020), 827-871, see here)
18. Two-microlocal regularity of quasimodes on the torus, with F. Macià (preprint, Analysis and PDE, Vol. 11, N°8 (2018), 2111-2136, see here)
19. Pollicott-Ruelle spectrum and Witten Laplacians, with N.V. Dang (preprint, J. Eur. Math. Soc., Vol. 23, N°6 (2020), 1797-1857, see here)
20. The quantum Loschmidt echo on flat tori, with H. Ueberschär (preprint, Nonlinearity, Vol. 32 (2019), 2094-2127, see here)
21. Equidistribution of toral eigenfunctions along hypersurfaces, avec H. Hezari (preprint,  Rev. Mat. Iberoam., Vol. 36 (2020), 435-454, see here)
22. Fried conjecture in small dimensions, with N.V. Dang, C. Guillarmou and S. Shen (preprint, Inventiones Math. Vol. 220 (2020), 525-579, see here)
23. Semiclassical asymptotics for nonselfadjoint harmonic oscillators, with V. Arnaiz (preprint, Pure and Applied Analysis Vol. 2 (2020), 427-445, see here)
    
24. Spectrum of a nonselfadjoint quantum star graph, with J. Royer (preprint, J. Phys. A: Math. Theor. Vol. 53 (2020), 495202, see here)
    
25. Poincaré series and linking of Legendrian knots, with N.V. Dang (preprint, to appear Duke Math. J. 173 (2024), 1--74, see here)
26. Local Lp norms of Schrödinger eigenfunctions on S^2 (preprint, Ann. Math. Québec Vol. 46 (2022), 93-119, volume in honour of A. Shnirelman, see here)
27. Dynamics of nonlinear Klein-Gordon equations in low regularity on S^2, with J. Bernier and B. Grébert (preprint, Annales de l'IHP C, Analyse Non Linéaire Vol. 40 (2023), 1009--1049, see here)
    
28. Length orthospectrum of convex bodies on flat tori, with N.V. Dang and M. Léautaud (preprint, Cambridge J. Math 11 (2023), 917--1043, see here)
    
29. Quantum limits of perturbed sub-Riemannian contact Laplacians in dimension 3, with V. Arnaiz (preprint, J. Ec. polytechnique 11 (2024), 909--956, see here)
    
30. Asymptotic regularity of sub-Riemannian eigenfunctions in dimension 3: the periodic case (preprint, to appear Contemporary Math., volume in honor of Steve Zelditch)
    
31. Nonlinear chaotic Vlasov equations, with Y. Chaubet et D. Han-Kwan (preprint)
32. Quantum unique ergodicity for magnetic Laplacians on T^2, with L. Morin (preprint)

• Notes/proceedings:

1. Entropy of semiclassical measures for quantized cat-maps (pdf, simplified version in the case d=1 of the article `Entropy of semiclassical measures for symplectic linear maps of the multidimensional torus', unpublished).
2. Entropie des mesures semi-classiques en dimension 2 (Actes du séminaire X-EDP, 2009, pdf).
3. Entropy of eigenfunctions of the Laplacian in dimension 2 (Actes des 37èmes Journées EDP, Port d'Albret 2010, pdf).
4. Observability and quantum limits for the Schrödinger equation on the sphere, with F. Macià (in Probabilistic Methods in Geometry, Topology and Spectral Theory, Contemporary Math. Vol. 739 (2019), AMS, pdf). 
5. Correlation spectrum of Morse-Smale gradient flows, with N.V. Dang (Actes des 44èmes Journées EDP, Roscoff 2017, pdf).
6. Dynamique de l'équation de Schrödinger sur le disque (d'après N. Anantharaman, M. Léautaud et F. Macià), Séminaire Bourbaki (70ème année, Exp. 1145, 2017-2018, pdf, in french)
7. Semiclassical behaviour of quantum eigenstates (pdf, lecture notes, Spring school "From quantum to classical", CIRM, 2019) Exercises
8. Length orthospectrum and the correlation function on flat tori, with N.V. Dang and M. Léautaud (preprint) (Actes des Journées EDP 2022, Obernai, pdf)

• Thesis (pdf): Phd thesis at the CMLS under the supervision of Nalini Anantharaman (defended on November, 25th 2009).
• Habilitation Thesis (pdf). Defended on October, 23rd 2017 (Lille).

• Correlation spectrum of Morse-Smale flows (talk at the CIRM, Conference Resonances: geometric scattering and dynamics, march 2017).
• Spectral analysis of Morse-Smale gradient flows (talk in Nantes, Summer school Analytical aspects of hyperbolic flows, july 2017).
• Dynamique de l'équation de Schrödinger sur le disque (talk at the IHP, Bourbaki seminar, march 2018).
• Witten Laplacian and Pollicott-Ruelle spectrum (talk in Banff, Workshop around quantum chaos, july 2018)
• Semiclassical behaviour of quantum eigenstates (lectures at the CIRM: parts 1 and 2, spring school From classical to quantum, april 2019).
• Poincaré series and linking of Legendrian knots (talk at the seminar Spectral Geometry in the Clouds, September 2021)

• ANR project Randomness, dynamics and spectra (2021-2025): more informations here.

• A day on quantum chaos took place in Université Lille 1 on December, 15th 2010 (the web page of the meeting is here).
• The 5th meeting of the GDR Quantum Dynamics took place in Lille from February 6th to February 8th 2013.
• Meeting of the ANR GERASIC (Lille, November 23 and 24, 2015)
• Workshop Spectral geometry, graphs and semiclassical analysis (Aussois, Dec. 11th to 15th, 2017)
• The 10th meeting of the GDR Quantum Dynamics took place in Lille from February, 21st to February, 23rd 2018.
• Workshop on microlocal analysis (Murramarang, Australie, March 18th to 23rd, 2018)
• Online seminar (spring and fall 2020)
• Semester Mathematical physics and geometry (Centre Henri Lebesgue, 2021)
• Conference in the honor of Didier Robert (Nantes, from May 26th to 28th 2025)

• 2007--2010: Tutorials in Ecole polytechnique
• 2010--2018: Lectures and tutorials in Université de Lille
• Since 2018: Lectures and tutorials in Université de Nantes