Finite quantum structures

Abstract: Weaver's quantum relations provide a basis for a unified understanding of several classes of quantum structures. In full generality, quantum relations are defined for arbitrary von Neumann algebras, but to simplify the discussion, this talk will focus on finite-dimensional von Neumann algebras. I will talk about quantum graphs, quantum posets, quantum groups, quantum metric spaces and quantum families of permutations and of graph isomorphisms. I will emphasize that each of these quantum generalizations can be motivated from Birkhoff and von Neumann's original conception of quantum logic as the logic of closed subspaces of a Hilbert space. (arXiv:2004.04377)

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides )

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.