Curvature for a class of noncommutative minimal surfaces

Abstract: The theory of minimal surfaces is an old and still quite active field of research, and it is natural to ask if there exists a corresponding theory in noncommutative geometry? In particular, analogues of minimal submanifolds appear in physical theories related to quantum gravity (string/membrane theory). I will present an approach to noncommutative minimal surfaces taking an equational point of view (rather than a variational one). After providing some background material leading to our definition of noncommutative minimal surfaces, I will discuss a framework for constructing Levi-Civita connections and curvature of such surfaces. These considerations naturally lead to a general discussion of metric connections on hermitian modules.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | 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.