Operator Algebras and Dynamics Seminars
Spring 2020
All talks are from 3:454:45 p.m. in the Seminar room, unless otherwise specified.

Apr29

[Postponed]Cesar SilvaWilliams CollegeTime: 03:45 PM

Apr20

[Postponed] Superstability and FiniteTime Extinction for C0SemigroupsDarren CreutzUSNATime: 03:45 PM
View Abstract
[Joint work with M. Mazo, Jr.] Semigroups of operators arise naturally in many areas, particularly Control Theory and PDEs. Specifically, a family of operators {T(t) : t >= 0} such that T(t+s) = T(t)T(s) and t > T(t) is strongly continuous is a C0semigroup and can always be realized as T(t) = exp(At) for some operator A, the infinitesimal generator. A C0semigroup is (exponentially) stable when for some M, omega > 0 and all t >= 0, T(t) <= M exp(omega t) and the maximal such omega is the stability index. Stable semigroups are the most useful and many equivalent characterizations (some of which I will mention) exist. Control theorists introduced the notion of superstable semigroups (circa 1990s), those where the stability index is infinite, having realized that finitetime extinction (T(t) = 0 eventually) occurred in many physical systems and clearly implies superstability. A natural question is whether superstability implies finitetime extinction. Balakrishnan (circa 2005) asked whether there exists a superstable semigroup with infinitesimal generator being a differential ("physical") operator that does not go extinct in finite time. We answer this question in the affirmative by introducing a variety of new machinery for studying the resolvent sets of the semigroup.

Apr13

[Postponed]Sayomi KamimotoLocation: George Washington UniversityTime: 03:45 AM

Mar30

[Postponed]Adam KanigowskiUniversity of MarylandTime: 03:45 PM