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Graduate Seminar Series

Wed., Mar. 29, 2023 3:30 p.m.

Location: CK 185 and Live Stream

Speaker: Patrick Melanson

Title: C^∗−Subproduct Systems, Kolmogorov Systems, and Limits (683 kB)

Abstract:

In this presentation, we introduce the idea of C^*−subproduct systems, one possible way to model sequential events or states. Explicitly, we work with families of C^*−algebras and the ^*−homomorphisms between them, satisfying certain associative properties. We discuss how to dilate these systems by forming a related direct (sometimes called inductive) system and taking the direct/inductive limit. We then use the same arguments to tackle Kolmogorov systems, which one can think of as the reverse of C^*−subproduct systems. In these systems we "glue" the spaces together, and thus we construct an inverse (or projective) system in an attempt to create an appropriate dilation.

Live Stream: