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Research
I study nonlinear partial differential equations, in particular Hamiltonian dispersive PDE and Navier-Stokes. My general interests are in analysis, probablity & stochastic differential equations.
Thesis
There exist data for which the focusing cubic nonlinear Schrödinger equation in three dimensions blows up on a ring. In higher dimensions, the proof establishes blowup on a set of co-dimension two.
Abstract | (pdf, 75Kb) | Full Text | (pdf, 604Kb) |
Teaching
Mat257, Fall 2009/Winter 2010 |
Course Homepage | |
Mat137, Summer 2009 |
Course Homepage |
Slides / Notes
January 21, 2010 |
Notes on potential minimal Navier-Stokes singularities. (pdf, 678Kb) |
About Me
A lantern shop in Vietnam,
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an alkaline lake and lava desert,
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bourgainvillia,
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enjoying a hike,
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a completely gratuitous portrait of poutine,
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summer on the Northumberland Strait,
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wearing a canoe on my head,
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and finally an insect,
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Links
- Colloquim, and Applied Math/PDE Seminar.
- The Fields Analysis Working Group, and Applied Math Colloquim.
- The less formal Dispersive Seminar, and Numerical PDE group.
- Dispersive Wiki, and Professor Colliander, my advisor.
- Magdalena Czubak, Tadahiro Oh, and Gideon Simpson, postdocs at Toronto.
- Terry Tao's Blog
Other
- TMU swim club.
- Toronto weather and traffic.
- Ontario winter driving conditions.