My name is Willie Wai-Yeung Wong, and I study geometric and evolutionary partial differential equations, with focus on those of hyperbolic type with applications to mathematical physics and general relativity. I received my PhD from Princeton University in 2009 under Sergiu Klainerman. My dissertation was about the black hole uniqueness problem in general relativity. Since then I’ve worked with Mihalis Dafermos at DPMMS, and at EPFL with Joachim Krieger. Currently I am an assistant professor at Michigan State University.
My current research focuses on
- Lorentzian constant mean curvature flow: the study of constant mean curvature Lorentzian hypersurfaces of Minkowski space from the point of view of the initial value problem (the constant mean curvature equations are hyperbolic PDEs). Main problems concern stability of exact/stationary solutions.
- Anisotropic second-order hyperbolic systems: extension of the theory of isotropic hyperbolic systems (in particular nonlinear wave equations) to the setting without isotropy. Main problems right now are: robust linear decay estimates, small data global wellposedness of quasilinear systems, shock formation.
- Singularity formation and classification: quantitative and qualitative descriptions of singularities, and notions of weak solutions for continuing past the singularity. Main problems include: construction of blow-up solutions to hyperbolic PDEs, stability of blow-up and threshold phenomenon, canonical weak evolution past singularities, geometry of the singular boundary.
- Geometric methods in hyperbolic PDEs and systems: interplay of the characteristic geometry of hyperbolic systems and the qualitative behaviour of solutions, with focus on the quasilinear setting. Main problems include: decay estimates for the wave equation on curved backgrounds with trapping, low regularity local wellposedness of systems, Carleman estimates and unique continuation for systems.
You can find my research papers, along with some slides and notes, on the Downloadables page.
If you’ve heard my name before it is probably because I used to moderate the discussion forum Mathematics Stack Exchange, and that I participate in MathOverflow. If not, then maybe you have me confused with someone else.
Here are some other places where I appear on the internet: