Research Interests

Nonlinear PDEs, integrable equations, asymptotic behavior of solutions, Cauchy problem, traveling waves, solitons, scattering transform method, inverse problems.

Publications and Preprints

• Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation - joint with C. Klein [preprint]
• Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II - joint with C. Muñoz [preprint]
• Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. Journal of Funct. Anal., 270(5), 1744-1791 (2016) - joint with C. Muñoz [printed version], [preprint]
• Absence of solitons with sufficient algebraic localization for the Novikov-Veselov equation at nonzero energy. Funct. Anal. Appl., 48(1), 24-35 (2014) [printed version], [preprint]
• Absence of conductivity-type solitons for the Novikov-Veselov equation at zero energy. Funct. Anal. Appl., 47(1), 64-66 (2013) [printed version], [preprint]
• A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with nonsingular scattering data. Inverse Problems, 28(5), 055017 (2012) [printed version], [preprint]
• Absence of exponentially localized solitons for the Novikov-Veselov equation at negative energy. Nonlinearity. 24, 1821-1830 (2011) - joint with R.G. Novikov [printed version], [preprint]
• Large time asymptotics for the Grinevich-Zakharov potentials. Bulletin des Sciences Mathematiques. 135, 374-382 (2011) - joint with R.G. Novikov [printed version], [preprint]
• A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy. J. Nonlinear Math. Phys. 18(3), 377-400 (2011) - joint with R.G. Novikov [pdf]
• Examples of the absence of a traveling wave for the generalized Korteweg-de Vries-Burgers equation. Moscow University Computational Mathematics and Cybernetics. 35(1), 14-21 (2011) [printed version]
• Stability of a traveling-wave solution of the Cauchy problem for the Korteweg-de Vries-Burgers equation. Comput. Math. Math. Phys. 50(4), 690-710 (2010) [printed version]
• Optimal strategies for reviewing search results. In proceedings of AAAI 2010. 1321-1326 (2010) - joint with J. Huang [pdf]
• Approximation algorithms for diversified search ranking. In proceedings of ICALP 2010. 273-284 (2010) - joint with N. Bansal , K. Jain , J. Naor [pdf]

Teaching

Maître de conférences (assistant professor) at University Paris-Sud, 2013-present

• Exercice sessions in Functional Analysis for 1st year master students (master 1) in ENSTA, 2015
• Exercice sessions in Linear Algebra for 2nd year undergraduate students (licence 2), 2015
• Exercice sessions in Evolution Problems for 1st year master students (master 1), 2013-present
• Exercice sessions in Differential Equations for 3rd year undergraduate students (licence 3), 2013-present
• Exercise sessions in Mathematical Analysis for 2nd year undergraduate students (licence 2), 2013-present

Teaching assistant in Applied Mathematics at Ecole Polytechnique, 2012-2013

• Practical sessions for the 2nd year students for the course "Numerical analysis and optimisation", 64h (miniproject "Lagrange problem on the optimal shape of a column: maximization of the first eigenvalue" )
• Optional course on FreeFem++ at Ecole Polytechnique for the 2nd and 3rd year students, ~15h, with Igor Favorsky

ParisMaths Olympiads Club exercise sessions, 2013-2014

• Here are some examples of distributed exercise sheets: homothety, invariants