I am currently the 'Chu' Assistant Professor at the department of Applied Physics and Applied Mathematics, Columbia University, New York.

I successfully defended my thesis May 31, 2011. The Ph.D. dissertation, entitled "Internal waves in oceanography and photonic crystals: a mathematical approach", is available here.

My current research interests focus on the mathematical modeling and rigorous study of various physical problems. An important part of my work is dedicated to the modelization of phenomenons arising in Oceanography, with a specific interest in the propagation of internal waves in stratified fluids. I also work on wave propagation in inhomogeneous media, and particularly in highly oscillatory microstructures.

Education

2008—2011 : Ph.D. Thesis in Applied Mathematics, Ecole Normale Supérieure de Paris.

Title: Internal waves in oceanography and photonic crystals: a mathematical approach.

Advisor: David Lannes.

Defense: March 31, 2011.

2007—2008 : Master Degree in Applied Mathematics at Université Bordeaux 1.

2006—2007 : Passed the Agrégation de Mathématiques.

2004—2008 : Student at the Ecole Normale Supérieure de Lyon.

Employment History

Feb. 2011: Staff Associate, Columbia University, New York.

Jan.-June 2008: Visiting Masters Student at Columbia University, New York. Scattering in random media.

Feb.-Aug. 2006: Visiting Masters Student at University of Freiburg (Germany). The multiscale finite element method.

June-Aug. 2005: Visiting Masters Student at the Université Lille 1 (France). Road traffic modeling.

Publications

[6]  (with I. Vukićević and M.I. Weinstein) Scattering and localization properties of highly oscillatory potentials, submitted. Preprint:hal-00655977

[5]  Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon, Nonlinearity, 24 (2011)

[4] (with M.I. Weinstein) Scattering, homogenization and interface effects for oscillatory potentials with strong singularities, Multiscale Model. Simul., 9 (2011)

[3]  Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation, M2AN Math. Model. Numer. Anal., 46 (2011)

[2] (with J. Marzuola and M.I. Weinstein) Wave operator bounds for 1-dimensional Schrödinger operators with singular potentials and applications, J. Math. Phys. 52 (2011)

[1]  Asymptotic shallow water models for internal waves in a two-fluid system with a free surface, SIAM J. Math. Anal. 42 (2010)

Communications

For selected talks, the presentation slides are accessible through the '.pdf' link, and accompanying documents (.tex, images, videos) through the '.zip' link.

Nov. 2009 : Journée de rentrée de l'équipe EDP, Paris.

Feb. 2010 : 2nd Workshop Mathematics and Oceanography, Montpellier. (.pdf,.zip)

May 2010 : Journée Nationale des Doctorants en Mathématiques, Amiens.

June 2010 : Workshop on Fluid Mechanics, Toulouse. (.pdf,.zip)

Nov. 2010 : Journée de rentrée de l’équipe EDP, Paris.

Feb. 2011 : Applied Mathematics Colloquium, New York. (.pdf,.zip)

Mar. 2011 : Workshop on PDEs and Numerical Analysis, Orsay.

Apr. 2011 : Séminaire des doctorants de Polytechnique, Palaiseau.

May 2011 : Mathématiques en Mouvement (talk for general audiences), Paris. (.pdf,.zip)

May 2011 : Workshop "Qualitative and numerical aspects of water waves and other interface problems", Vienne.

June 2011 : Conférence "Analyse de modèles en mécanique des fluides", Nice.

Sept. 2011 : APAM Friday Research Conference, Columbia University, New York.

Oct. 2011 : Seminar in Applied Mathematics (lecture to junior and senior Applied Mathematics majors), Columbia University, New York.

Oct. 2011 : Courant Analysis seminar, New York University, New York.

Dec. 2011 : Geometry and Analysis Seminar, Columbia University, New York. (.pdf,.zip)

Mar. 2012 : Lefschetz Center for Dynamical Systems Seminar, Brown University.

Apr. 2011 : Numerical Analysis and PDEs Seminar, Laboratoire Paul Painlevé, Lille.

Teaching

Website of APMA E4001: Principles of Applied Mathematics

University Paris 6 (2008—2011)

LM110: Analyse 1 -- Fonctions

LM250: Suites, séries et intégrales

LM260: Séries et intégrales (étude approfondie)

Columbia University (2011—...)

APMAE3101: Linear Algebra

APMAE4001: Principles of Applied Mathematics

Contact

Applied Physics and Applied Mathematics (APAM), Columbia University
#203 S.W. Mudd Building (Mail Code: 4701)
New York, NY 10027

E-mail: vd2202[at]columbia(dot)edu
Phone: (212)-854-4953