Nonnoetherian geometry, noncommutative desingularizations, and quantum theory

Abstract: I will introduce a new kind of geometry that arises from nonnoetherian subalgebras of polynomial rings, and, more generally, coordinate rings of affine varieties. In this construction, points may be 'smeared-out' and have positive dimension. I will then describe an application of this geometry to a class of noncommutative algebras defined by oriented graphs in surfaces, called dimer and ghor algebras. The geometry allows these algebras to be viewed as noncommutative desingularizations of their centers, and yields relationships between their representation theory and the surface topology. Finally, I will sketch an application of the geometry to a new spacetime model of spin and its wave function collapse.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )

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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 meet.google.com/zjd-ehrs-wtx (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.

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