Gabriel Rivière

Version françaiseMaître de Conférences

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

UFR de Mathématiques

Université de Lille 1

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)

- 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).

- 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).
- 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 Lille 1(see here for details)

CV (december 2017, in french)