Operator Algebras and Dynamics Seminars

Spring 2020

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

• Apr

  29
• [Postponed]

  Cesar Silva

  Williams College

  Time: 03:45 PM

• Apr

  20
• [Postponed] Superstability and Finite-Time Extinction for C0-Semigroups

  Darren Creutz

  USNA

  Time: 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 C0-semigroup and can always be realized as T(t) = exp(At) for some operator A, the infinitesimal generator. A C0-semigroup 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 finite-time extinction (T(t) = 0 eventually) occurred in many physical systems and clearly implies superstability. A natural question is whether superstability implies finite-time 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.

• Apr

  13
• [Postponed]

  Sayomi Kamimoto

  Location: George Washington University

  Time: 03:45 AM

• Mar

  30
• [Postponed]

  Adam Kanigowski

  University of Maryland

  Time: 03:45 PM