Gabriel Rivière
Version française

Maître 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

  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, to appear J. Eur. Math. Soc.) 
  14. Spectral analysis of Morse-Smale gradient flows, with N.V. Dang (preprint)
  15. Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces, with N.V. Dang (preprint)
  16. Spectral analysis of Morse-Smale flows II: resonances and resonant states, with N.V. Dang (preprint)
  17. Topology of Pollicott-Ruelle resonant states, with N.V. Dang (preprint)
  18. Two-microlocal regularity of quasimodes on the torus, with F. Macià (preprint)
  19. Pollicott-Ruelle spectrum and Witten Laplacians, with N.V. Dang (preprint)
  20. The quantum Loschmidt echo on flat tori, with H. Ueberschär (preprint)
  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 (to appear CRM Proceedings  Probabilistic methods in spectral theory and PDE 2016, pdf). 
  5. Correlation spectrum of Morse-Smale gradient flows, with N.V. Dang (Actes des 44èmes Journées EDP, Roscoff 2017, pdf).


Teaching

CV (december 2017, in french)