Research

“Inspiration is for amateurs—the rest of us just show up and get to work.”

—Chuck Close (as quoted in Joe Fig, Inside the painter’s studio, Princeton Architectural Press, 2009, p. 42).

“My working method has more often than not involved the subtraction of weight.”

—Italo Calvino, Six Memos for the Next Millennium, Harvard University Press, 1988, p. 3.

“Un des progrès les plus significatifs de l’enseignement instrumental, au cours de ces dernières années, a consisté à remplacer l’exercice mécanique et longuement répété d’un passage difficile par l’étude raisonnée de la difficulté qu’il contient, ramenée à son principe élémentaire.”

—Alfred Cortot, Principes Rationnels De La Technique Pianistique, Éditions Salabert, 1930, p. 1.

My main research interests lie in applied analysis and partial differential equations.

More specifically, my work includes:

hyperbolic conservation laws, motivated by traffic flow and continuum mechanics, including nonlocal effects or dynamics on networks: well-posedness, singular limits, long-time behavior, control, stabilization, inverse problems, numerical approximation possibly using machine learning approaches;

fluid flows and irregular transport: (weak) regularity and mixing phenomena for transport equations with rough coefficients, (ir)regularity and (in)stability for fluid models, long-time behavior, computational study of singularities, control, stabilization, and inverse problems;

nonlinear waves, arising in elasticity or dispersive phenomena, including dynamics on networks: well-posedness, (in)stability properties, long-time behavior, control, stabilization, and inverse problems;

parabolic equations, including degenerate or nonlocal models, with cross-diffusion effects or posed on networks: well-posedness, long-time behavior, interface propagation phenomena, and symmetry properties;

calculus of variations and variational methods for nonlinear elliptic problems, their asymptotic analysis, functional inequalities and their stability, symmetry (breaking), and concentration phenomena.

Here is the list of my papers.

Here is the list of grants that have supported my work.