My research focusses on the interaction between geometry and partial differential equations (PDEs). Mainly my current interests can be described by one of two banners: (1) applying view-points and methods from (differential/pseudo-Riemannian/something else) geometry to the study of hyperbolic PDEs; and (2) solving inherently geometric problems by looking at their associated PDEs. An example of the former is my work on shock formation for quasilinear wave equations. Examples of the latter include my work in general relativity, as well as my work studying time-like constant mean curvature submanifolds of Minkowski space.

Selected Publications

Jared Speck, Gustav Holzegel, Jonathan Luk, and Willie Wong. "Stable shock formation for nearly simple outgoing plane symmetric waves." To appear in Annals of PDE. (arXiv:1601.01303)

Willie Wong. "Global Existence for the Minimal Surface Equation on R^{1,1}." To appear in Proc. Amer. Math. Soc., Ser. B. (arXiv:1601.01096)

Gustav Holzegel, Sergiu Klainerman, Jared Speck, and Willie Wong. "Shock formation in small-data solutions to 3D quasilinear wave equations: an overview." J. Hyperbolic Diff. Eq. 13, 1--105 (2016).

Roland Donninger, Joachim Krieger, Jeremie Szeftel, and Willie Wong. "Codimension one stability of the catenoid under thevanishing mean curvature flow in Minkowski space." Duke Math J. 165, 723--791 (2016).

Willie Wong and Pin Yu. "Non-existence of multiple-black-hole solutions close to Kerr-Newman." Comm. Math. Phys. 325, 965--996 (2014). (arXiv:1210.1379)