Long Term Research Interests:
 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.
I received the Medal of Science in Washington, December 1, 2000.(Here are some photos)
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: I gave the Ritt lectures at Columbia in April 2002. Here is an (abstract).

Newest:    Here is an abstract for my talk at the Yamabe Symposium in September 2004.

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).