Gabriel Rivière

Version françaiseMaître de Conférences

Laboratoire Paul Painlevé (U.M.R. CNRS 8524)

Département de Mathématiques

Faculté des sciences et technologies

Université de Lille

59 655 Villeneuve d'Ascq Cédex

France

Bâtiment M3, Bureau 222

Tel: 00 33 (0)3 20 43 67 38

Courriel: gabriel.riviere(the symbol)math.univ-lille1.fr

Research

- Research topics: semiclassical analysis, dynamical systems, mathematical physics.

- Research articles: (the published version may slightly differ from the preprint version)

- Entropy of semiclassical measures in dimension 2 (preprint, Duke Math. J., Vol. 155, N° 2 (2010), 271-335, see here).
- Entropy of semiclassical measures for nonpositively curved surfaces (preprint, Annales Henri Poincaré, Vol. 11, N°6 (2010), 1085-1116, AHP Distinguished Paper, see here).
- 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).
- 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).
- Delocalization of slowly damped eigenmodes on Anosov manifolds , (preprint, Comm. in Math. Phys., Vol. 316, N°2 (2012), 555-593 see here).
- 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).
- Remarks on quantum ergodicity, (preprint, Journal of Modern Dynamics, Vol. 7, N°1 (2013), 119-133 see here).
- 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)

- Lp norms, nodals sets, and quantum ergodicity, with H. Hezari (preprint, Adv. Math., Vol. 290 (2016), 938-966, see here)
- 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)
- Quantitative equidistribution properties of toral eigenfunctions, with H. Hezari (preprint, J. Spectral Theory, Vol. 7 (2017), 471-485, see here)

- 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)
- Equidistribution of the conormal cycle of random nodal sets, with N.V. Dang (preprint, to appear J. Eur. Math. Soc.)
- Spectral analysis of Morse-Smale gradient flows, with N.V. Dang (preprint)
- Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces, with N.V. Dang (preprint)
- Spectral analysis of Morse-Smale flows II: resonances and resonant states, with N.V. Dang (preprint)

- Topology of Pollicott-Ruelle resonant states, with N.V. Dang (preprint)
- Two-microlocal regularity of quasimodes on the torus, with F. Macià (preprint)
- Pollicott-Ruelle spectrum and Witten Laplacians, with N.V. Dang (preprint)
- The quantum Loschmidt echo on flat tori, with H. Ueberschär (preprint)
- Equidistribution of toral eigenfunctions along hypersurfaces, avec H. Hezari (preprint)

- Notes/proceedings:

- 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).
- Entropie des mesures semi-classiques en dimension 2 (Actes du séminaire X-EDP, 2009, pdf).
- Entropy of eigenfunctions of the Laplacian in dimension 2 (Actes des 37èmes Journées EDP, Port d'Albret 2010, pdf).
- Observability and quantum limits for the Schrödinger equation on the sphere, with F. Macià (to appear CRM Proceedings Probabilistic methods in spectral theory and PDE 2016, pdf).
- Correlation spectrum of Morse-Smale gradient flows, with N.V. Dang (Actes des 44èmes Journées EDP, Roscoff 2017, pdf).
- Dynamique de l'équation de Schrödinger sur le disque (d'après N. Anantharaman, M. Léautaud et F. Macià), Séminaire Bourbaki (70ème année, Exp. 1146, 2017-2018, pdf, in french)

- 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).

- 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 will be held in Lille from February, 21st to February, 23rd 2018.
- Workshop in microlocal analysis (Murramarang, Australie, March 18th to 23rd, 2018)

Teaching

- 2007/2010: Tutorials in Ecole polytechnique
- Since 2010: Lectures and tutorials in Université de Lille (see here for details)

CV (february 2018, in french)