| * Venue | Media Centre |
| * Speaker | Piyasa Sarkar |
| * Title | On Multi-parameter CCR flows |
| Affiliation | IMSc (HBNI) |
| Abstract | $E_0$-semigroups were introduced by R.T. Powers in the late nineteen-eighties and has since been an interesting and productive area of research. An $E_0$-semigroup over $[0, \infty)$ is a semigroup of unital, normal $*$-endomorphisms of $B(H)$, for some Hilbert space $H$, that also satisfy some continuity conditions. In this talk, we focus on a class of $E_0$-semigroups called CCR flows. One-parameter CCR flows were completely characterised by Arveson using a numerical invariant called the "index". Later, multiparameter CCR flows over closed convex cones were dealt with by Arjunan et al. I will speak about multiparameter CCR flows in the context of Lie semigroups, comparing our results to those of Arjunan's, and proving the injectivity of the CCR functor in this context. We also extend the definition of index to the multiparameter case. In the later half, I shall introduce induced isometric representations and use them to construct prime type I multiparameter CCR flows over closed convex cones in $\mathbb{R}^d$, having index $k$, for any $k \in \mathbb{N} \cup \{\infty\}$. |
| * Announcement? | Institute |
| * Refreshments? | None |
| * Honorarium? | None |
| Special Arrangements? | None |
| * Host name and email | S Sundar @@ ssundar@imsc.res.in |