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Tristan Robert's Personal Page

Contact

Office 123 Office 114
IECL - Nancy Campus Department of Computer Science
Faculty of Science and Technology IUT Nancy-Charlemagne
Campus, Boulevard des Aiguillettes 2 ter Boulevard Charlemagne
54506 Vandoeuvre-lès-Nancy 54000 Nancy

Biography

Since 2021, I have been a "Maître de conférences" (~associate professor) at the University of Lorraine, where I teach in the Department of Computer Science at IUT Nancy-Charlemagne.

In 2020-2021, I was an "Agrégé Préparateur" (~assistant professor) at ENS Rennes.

In 2019-2020, I was a Postdoctoral Researcher under the supervision of Sebastian Herr at the University of Bielefeld (Germany), where I worked on dispersive PDEs in the presence of randomness.

From September 2018 to August 2019, I was a Postdoctoral Researcher at the University of Edinburgh (UK), where I collaborated with Tadahiro Oh on the Cauchy problem for nonlinear dispersive equations with random data and/or stochastic source terms, and also on the construction of Gibbs measures for these models.

I completed my PhD at the University of Cergy-Pontoise from 2015 to 2018 under the supervision of Nikolay Tzvetkov. I studied the use of small-time Bourgain spaces to prove the well-posedness of the Cauchy problem for quasi-linear dispersive PDEs, specifically for Kadomtsev-Petviashvili-type models, with applications to the study of the orbital stability of solitons.

A detailed curriculum vitae is available here.

Research Interests

Articles and Preprints

    Dynamics of Hamiltonian PDEs

  1. (with J. Bernier and B. Grébert) Infinite dimensional invariant tori for nonlinear Schrödinger equations.
  2. (with J. Bernier and B. Grébert) Dynamics of quintic nonlinear Schrödinger equations in H^(2/5+)(T), to appear in Tran. AMS (2025) ([arXiv])

    3. Regularization by Noise

  3. On the Kadomtsev-Petviashvili equations with rough dispersion management, in preparation.
  4. Regularization by noise for some strongly non-resonant modulated dispersive PDEs.
  5. Remarks on nonlinear dispersive PDEs with rough dispersion management.

    6. Invariant Measures and Singular Stochastic PDEs

  6. (with Y. Zine) Stochastic complex Ginzburg-Landau equation on compact surfaces.
  7. (with H. Eulry and A. Mouzard) Anderson stochastic quantization equation.
  8. (with T. Oh, N. Tzvetkov, and Y. Wang) Stochastic quantization of Liouville conformal field theory.
  9. (with K. Seong, L. Tolomeo, and Y. Wang) Focusing Gibbs measures with harmonic potential, Ann. Inst. H. Poincaré Probab. Statist. (2025) ([arXiv])
  10. (with I. Bailleul and H. Eulry) Variational methods for some singular stochastic elliptic PDEs, Ann. Fac. Sci. Toulouse Math. (2024) ([arXiv])
  11. Invariant Gibbs measure for a Schrödinger equation with exponential nonlinearity, J. Funct. Anal. (2024) ([arXiv])
  12. (with T. Oh and N. Tzvetkov) Stochastic nonlinear wave dynamics on compact surfaces, Annales Henri Lebesgue 6 (2023), 161-223. ([arxiv])
  13. (with T. Oh, P. Sosoe, and Y. Wang) Invariant Gibbs dynamics for the dynamical sine-Gordon model, Proc. Roy. Soc. Edinburgh Sect. A. 68 (2020), 1-17. ([arXiv])
  14. (with T. Oh and Y. Wang) On the parabolic and hyperbolic Liouville equations, Comm. Math. Phys. 387 (2021), 1281–1351. ([arXiv])
  15. (with T. Oh, P. Sosoe, and Y. Wang) On the two-dimensional hyperbolic stochastic sine-Gordon equation, Stoch. Partial Differ. Equ. Anal. Comput. (2020). ([arXiv])
  16. (with T. Oh and M. Okamoto) A remark on triviality for the two-dimensional stochastic nonlinear wave equation, Stochastic Processes and their Applications (2020). ([arxiv])

    17. Cauchy Problem for Nonlinear Dispersive PDEs

  17. (with F. Linares, M. Panthee, and N. Tzvetkov) On the periodic Zakharov-Kuznetsov equation, Discrete Contin. Dyn. Syst. 39 (2019), no. 6, 3521–3533. ([arXiv])
  18. Remark on the semilinear ill-posedness for a periodic higher order KP-I equation, C. R. Math. Acad. Sci. Paris 356 (2018), no. 8, 891–898. ([arXiv])
  19. On the Cauchy problem for the periodic fifth-order KP-I equation, Differential Integral Equations 32 (2019), no. 11-12, 679–704. ([arXiv])
  20. Global well-posedness of partially periodic KP-I equation in the energy space and application, Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, 1773–1826.([arXiv])

Miscellaneous

Talks

Conferences Attended