My research lies at the overlap of Nonlinear Fourier Analysis/Harmonic Analysis and Nonlinear Partial Differential Equations integrating into it tools from geometry, gauge theory and probability. In recent years, its main focus has been to investigate: (i) the behavior of solutions to nonlinear dispersive equations arising as models both in Physics and in Geometry -both from a deterministic and nondeterministic viewpoint and (ii) wave-packet analysis techniques and multilinear singular pseudodifferential operators naturally arising in Analysis and PDE. These are two areas that intimately relate to each other by way of decompositions, frequency interactions analysis and nonlinear estimates.
No subject area
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS (with Tadahiro Oh, Luc Rey-Bellet, and Gigliola Staffilani), JEMS (2010)
In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative...
On the well-posedness of the wave map problem in high dimensions (with Karen Uhlenbeck and Atanas Stefanov), Communications in Analysis and Geometry (2003)
We construct a gauge theoretic change of variables for the wave map from R ×...