Operator Algebras
Operator Theory
Functional Analysis
Matrix Analysis
Classification of C*-algebras has
Last two decades a lot have been studied about the polynomials with noncommuative variables. In particular, polynomial functions on some matrix algebras. These turn out to be very important in quantum mechanics for eigenvalue minimization and trace minimization. This relates to a lot of different subjects including real algebraic geometry, control theory and functional analysis. My recent endeavour to go through th research work of Igor Klep and other collaborators has directed me to sum of squares, semidefinite programming and optimization problems. I am currently exploring the connection of it with real algebraic geometry.
Most of the topics during my PhD that I have studied are related to C*-algebra and its classifications.