The Professor Vishnu Vasudeva Narlikar Memorial Lecture (of the Indian National Science Academy) for the year 2021, organised jointly by the Indian Institute of Science (IISc) and DBT-Institute for Stem Cell Science and Regenerative Medicine (inStem), will be delivered by Prof. B V Rajarama Bhat (ISI Bangalore) in the Department of Mathematics, IISc. The details are as follows.

**Title.** â€‹Dilation theory of quantum dynamical semigroups

**Date and Time.** March 20, 2023 (Monday), 4 pm

**Venue.** LH-1, Mathematics Department

**Abstract.** Often, mathematical structures or dynamics can be understood better when they are treated as projections of bigger, more easily understood systems. In quantum theory of open systems, the dynamics is described through quantum dynamical semigroups. They are non-commutative analogues of stochastic maps. Classically, we have Kolmogorovâ€™s construction for stochastic transition semigroups. In a similar fashion, starting with quantum dynamical semigroups one can construct quantum Markov processes. Going further by considering the shift on these processes, one obtains semigroups of endomorphisms. This has led to new understanding of tensor product systems of Hilbert spaces. We will outline some highlights of this theory.

Last updated: 08 Dec 2023