My main research interests are in operator algebras, operator theory and functional analysis. My work is also related to dynamical systems and non-commutative convex algebraic geometry.
More specifically, I study various operator structures and their interactions with some underlying combinatorial, dynamical or geometric object. These include Markov chains, directed graphs, completely positive maps, subshifts and semigroup dynamical systems.
I am also interested in matrix convex sets and their connection to operator systems, where these often yield interesting applications to convex optimization and quantum information theory.