Ted Voronov: Supergeometry and the (Frobenius-Kolmogorov-Gelfand-) Buchstaber-Rees theory
|Starts:||14:30 6 Feb 2020|
|Ends:||15:30 6 Feb 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers|
Title: Supergeometry and the (Frobenius-Kolmogorov-Gelfand-)Buchstaber-Rees theory
Victor Buchstaber and Elmer Rees, motivated by the study of n-valued groups, introduced a generalization of ring homomorphisms under the name of "Frobenius n-homomorphisms". (Because of the connection with Frobenius's work on "higher characters".) Their central geometric result is an extension of the Gelfand-Kolmogorov theorem---describing a topological space in terms of its algebra of continuous functions---to symmetric powers of a topological space. It turns out that ideas from supergeometry can help to simplify and generalize the theory of Buchstaber and Rees. (I do not mean by that a "superanalog".) The ideas come from our study of Berezinians and super exterior powers. Very roughly, while the Buchstaber-Rees theory tells what a sum of ring homomorphisms is (as everybody knows, it is not a homomorphism), our theory tells what the difference or actually an arbitrary integral linear combination of ring homomorphisms are.
The talk is based on joint works with H. Khudaverdian. We were brought to recall these works recently because of passing away of Elmer Rees in October 2019 (to whose memory the talk is dedicated).
Organisation: University of Manchester
Travel and Contact Information
Frank Adams Room 1
Alan Turing Building