I currently work on the following areas in mathematical physics:
Kinetics of phase transitions and models of domain coarsening.
Integrable systems and random matrix theory.
Statistical theories of turbulence.
The common theme in my work in these areas is the use of integrable systems.The methods of integrable systems bridge several areas of mathematics, linking deep algebraic structure with powerful computational techniques. I am mainly interested in the unexpected appearance of integrable structures in several probabilistic models. I am also interested in the construction of random fields in several applications (in particular, random surfaces and turbulent fluid flows). If you're a beginning or prospective grad student and you don't know what these words mean, here is a rough translation: I prove theorems about ensembles of solutions to various equations of physical importance. My work is roughly at the intersection of dynamical systems, PDE and probability theory.
I am also fascinated with the idea that biology can inspire nanotechnology. I collaborate with several labs on the use of self-assembly to design containers, devices and supramolecular assemblies. Here is a link to a brief documentary explaining part of our work. Interested in a longer explanation? Here is my talk at the Frontiers of Science meeting in 2012. My work on self-assembly involves mainly modeling and scientific computation, but there is certainly interesting mathematical structure to be discovered.
If you are a high school student interested in Brown's applied math program, and would like to meet someone during your visit, our Departmental Undergraduate Group can help.
We offer several opportunities for undergraduates to get involved in research. In addition to summer REUs , consider taking an independent study class or a senior seminar during the academic year. This is a simpler commitment for many faculty since it does not involve summer travel or funding (which is often closed to foreign students).
I have worked with several undergraduates and am happy to serve as an advisor for an honors thesis. My typical expectation is that you work with me for at least two semesters, commiting time equivalent to at least one class per semester. I do not fund summer "internships" for international students.
If you are a prospective student, here are some facts to consider. Our work is interdisciplinary: we have two departments with mathematicians, a wonderful mathematics institute, close ties to several other departments across campus and a strong pool of students. I am happy to respond to specific inquiries about working with me (are you advising new students? what should my preparation be? etc.). All questions on admissions are best addressed to our graduate committee (for example, please do not ask me to assess your chances of getting into our program).
On a more humorous note, I am no longer accepting portfolios from prospective Bollywood stars. Yes, I receive such portfolios --such is the curse of the internet. Google will tell you why.
BU/Brown PDE seminar. , Wednesday afternoons, once a month.
LCDS seminar, Monday, 4-5pm.
PDE seminar, Friday, 3-4 pm.
Pattern theory seminar , Wednesday, noon-1pm.
Probability seminar .