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’einsegnement instrumental, au cours de ces dernières anneés, a consisté à remplacer l’exercice mechanical et longuement répété d’un passage difficile par l’étude raisonnée de la difficulté qu’il contient, remanée 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, I’ve been working on the following topics:

  • hyperbolic conservation laws;
  • nonlinear waves;
  • fluid flows and irregular transport;
  • local and nonlocal (nonlinear, degenerate, higher-order) parabolic PDEs;
  • free boundary problems;
  • controllability, optimization, and stabilization problems;
  • calculus of variations and variational methods for the study of nonlinear (elliptic) problems;
  • mathematical methods in machine learning.

Here is a list of my papers.