My primary research interest is Operator Algebras. So far, my research has been centerned around Arveson's hyperrigidity conjecture. I have studied certain unique extension property of *-representations of a C*-algebra (relative to an operator system) via some partial orders defined on the state space of the C*-algebra. A detailed account of my first research work can be found here.
Choquet order is a partial order defined on the set of all regular Borel probability measures on a compact convex set (subset of a locally convex topological vector space). Davidson and Kennedy established a connection between Choquet order and the hyperrigidity of operator systems in a commutative C*-algebra. In an ongoing solo project, I am trying to extend the definition of Choquet order to the state space of non-commutative C*-algebras. By analogy with the classical commutative case, I expect that these new relations can eventually serve as meaningful tools in studying the structure of general operator systems.
I am also motivated to broaden my knowledge and explore other related branches, such as non-commutative function theory, non-commutative geometry, C*-dynamical systems, von-Neumann algebras, quantum information theory etc.