Research

“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 the analysis and control of partial differential equations. More specifically, I’ve been working on the following topics:

  • hyperbolic conservation laws;
  • transport with rough velocity fields;
  • flows on networks;
  • (dissipative) hyperbolic PDEs;
  • local and nonlocal degenerate (higher-order) parabolic PDEs;
  • free boundary problems;
  • variational and topological methods for the study of nonlinear problems.

Here is a list of my papers.