Long Term Research Interests:

- Geometric Partial Differential Equations
- The Calculus of Variations, especially scale invariant problems (past interest)
- Gauge Theory (now mostly for wave and non-linear Schoedinger systems)
- Integrable Systems
- Virasoro actions
- Non-linear waves and non-linear Schroedinger Equations, especially scale invariant problems

Research Group:

I am a member of the geometry group in the mathematics department. The geometry group maintains a website with general and current information (click here). We have three weekly seminars. Gadget is an informal seminar which meets for lunch Tuesday from 12:30 to 2:00. Students are particularly urges to attend this seminar. There is also a joint seminar with the high energy physics group Wednesday at 1:00, and a formal research seminar on Thursdays from 3:30-5:00. Students are particularly urged to attend both the Gadget seminar and the first hour of the formal seminar. The formal seminar is split into two parts, and speakers are really expected to give an expository talk during the first hour. Only specialists usually stay for the second half.

These pictures were taken at the ceremony . You will see Efraim Armendariz, Ingrid Daubechies, Dick Palais, Jean Taylor, Chuu-Lian Terng , Bob Williams and S.T. Yau, who all came to the ceremony.Newer:

(abstract)

Recent research:

My recent research has been mainly on two subjects, with two groups of coauthors. I have written four papers of with Chuu-Lian Terng on the geometric aspects of integrable systems. With Andrea Nahmod and Atanas Stefanov I authored two papers on wave maps and Schoedinger maps. These are all posted on the LANL preprint server (in geometry or anaylsis).