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# Graduate Seminar Series

**
Wed., Mar. 29, 2023 3:30 p.m.
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Location: CK 185 and Live Stream
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**Speaker**: Patrick Melanson

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

**Abstract:**

*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:**

https://uregina-ca.zoom.us/j/94125367372