Algebraic Geometry
PASECHNIK, Dmitrii V
He studies a range of topics related to computing on semialgebraic sets, in particular semidefinite programs (SDP). This includes algebraic techniques for dimension reduction of SDPs, SDP relaxation techniques for computationally intractable problems, and exact symbolic computing over R, including complexity questions. As well, he is interested in combinatorics, algebraic geometry (mostly real), and group theory.