Benjamin Pineau

Benjamin Pineau will be joining the Courant Institute at New York University as a postdoctoral fellow and will be working under the mentorship of professor Vlad Vicol. Pineau is completing his Ph.D. in mathematics at the University of California, Berkeley under the supervision of professor Daniel Tataru. Previously, he completed his BSc. in mechanical engineering at the University of Alberta.

Pineau’s work during his Ph.D. can be broadly divided into three categories. The first is in free boundary problems, where one seeks to understand the evolution of a fluid when the motion of its domain is strongly coupled to the flow. Classical examples include the dynamics of water waves or gaseous stars. A second class of problems is concerned with nonlinear dispersive equations, where one is interested in understanding the behavior of nonlinear wave interactions. In this area, Pineau has worked on the low regularity theory for certain classes of quasilinear Schrödinger equations which, for instance, serve as models for some phenomena arising in fluid mechanics and magnetohydrodynamics. A third subject Pineau has worked on, unrelated to PDE, is phase retrieval. Here, one is roughly concerned with understanding when functions (sampled from some restricted subspace) can be reconstructed from their absolute value (modulo a global phase). One physically motivated scenario in which this arises is crystallography.