Post-doc at Georgia Institute of Technology
ruoci.sun.16@normalesup.org
My mentor is Prof. Zhiwu Lin.
Research Interests:
Partial differential equations, Integrable Systems, Mathematical physics
My research interest focuses on integrable systems and partial differential equations (PDEs). Precisely, I work on the construction of (generalized) action--angle coordinates, Birkhoff coordinates and explicit expression of solutions of integrable systems. I am also interested in the long time behavior of solutions of PDEs including the wave turbulence phenomena, the nonlinear scattering phenomena, the soliton resolution conjecture, the stability and instability of traveling waves.
Publications and preprints:
arXiv:2310.13693: Matrix solutions of the cubic Szegő equation on the real line, preprint.
hal-04227081: The intertwined derivative Schrödinger system of Calogero--Moser--Sutherland type, Lett. Math. Phys. 114, 74. (2024).
arXiv:2309.12136: The matrix Szegő equation, preprint.
arXiv:2004.10007: Complete integrability of the Benjamin--Ono equation on the multi-soliton manifolds, Commun. Math. Phys. 383 (2), 1051-1092
arXiv:1912.10889: Filtering the L^2-critical focusing Schrödinger equation, Discrete Contin. Dyn. Syst. A 40, (2020) No. 10, 5973-5990.
arXiv:1904.09182: Long time behavior of the NLS-Szegö equation, Dyn. Partial Differ. Equ. 16 (2019), No.4, 325-357.
Sur le rayon des solutions analytiques de l'équation de Schrödinger non linéaire défocalisante (pdf)
Sur le domaine d’analyticité de la solution de l’équation de Schrödinger non linéaire intégrable (Master Thesis)
Training:
2016-2020 : PhD of Mathematics, Université Paris-Saclay
Advisor: Patrick Gérard
2013-2016 : Ecole Normale Supérieure (Paris)
Teaching:
Georgia Tech:
KIT:
Introduction to Microlocal Analysis
Université Paris-Saclay
L1:
Math101 Calculus
L2:
Math203 Analyse et Algèbre 2
TD1 TD2 TD3 TD4 TD5 TD6 TD7 TD8
Math250 Matrices & équations différentielles
TD1 TD2 TD3 TD4 TD5 TD6 TD7 TD8
Math256 Analyse pour physiciens
Math259 Algèbre pour physiciens