Lecture on multiparameter E_0-semigroups

The Department of Mathematics at SRM University-AP is conducting a departmental seminar on November 24, 2021, at 3:00 pm. Prof Sundar Sobers from The Institute of Mathematical Sciences, Chennai, India will engage the participants on the topic “Multiparameter E_0-semigroups”.

Abstract of the lecture:

In the late eighties, Powers initiated the study of the 1-parameter semigroup of endomorphisms on B(H). This was further studied intensively by many others during the last three decades led by William Arveson. Although from the physics point of view, the 1-parameter theory is the most important one, from the mathematical perspective, it is not necessary to restrict oneself to 1-parameter, i.e. the half-line [0,\infty) and we could replace the half-line with any reasonable semigroup’ like convex cones in higher-dimensional Euclidean space. One of the nice features is that the basic theory stays intact while there are significant differences between the 1-parameter theory and the n-parameter theory. I will explain one such phenomenon.

In particular, Prof Sundar Sobers will define the basic examples of E_0-semigroups, i.e. the CCR and CAR flow associated with isometric representations of the semigroup P. In the multiparameter world, CCR flows need not be isomorphic to its opposite, a sharp contrast to the one-parameter situation.

Don’t forget to join this lecture on November 24, 2021, at 3:00 pm which will be helpful to participants who are doing or planning to start a career in the multiparameter E_0-semigroups domain.