Specific research interests: Theory of error-correcting codes,
Approximation algorithms and hardness of approximation results for optimization problems, Theory of pseudorandomness, Probabilistically Checkable Proofs,
Complexity Theory, Algebraic algorithms.
Here are brief descriptions about my two main research focuses (these
are dated and have not been updated with recent developments, but may still useful to get a broad picture):
Approximate
solutions to NP-hard problems (in the last few years, much
exciting progress has been made by the theory community on some of the
"favorite" problems mentioned at the end of the
description; see also Raghavendra's Ph.D. talk linked below)