I have three research areas: (a) semantics and logics for
probabilistic systems (b) logic and computation and (c)
machine learning. I work on approximation of
continuous-state systems and associated metrics and logics.
I am working on a quantitative extension of equational logic
which allows one to carry out approximate reasoning.
I have been working on Stone duality for Markov processes and
completeness theorems for Markovian logics. I am also
interested in duality for automata and using it for
minimization. Recently I have begun working on approximate
minimization. I am also interested in Tannaka-type theorems
for C* algebras. I have occasionally made forays into
general relativity and quantum mechanics, the subject of my
PhD thesis which continues to interest me.
Samson Abramsky, Anuj Dawar, Phokion
Kolaitis and I organized a thematic semester on
at the Simons
Institute for Theoretical Computer Science in
boards on which I serve are accessible
through Links above.