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.
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.
(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).