The structure of KMS states for flows on an AF algebra

Abstract: In a recent work with George Elliott we have obtained a complete description of the configurations of KMS states that occur for flows on a unital simple infinite dimensional AF algebra. The answer is that they all do, provided only that the simplex of 0-KMS states is affinely homeomorphic to the tracial state space of the AF algebra; a condition which is obviously necessary. In the talk I will explain the road to this conclusion, which can be seen as the culmination of work and ideas that go back more than 40 years and has involved very many mathematicians.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.