College of Liberal Arts and Sciences

# Department of Mathematics

## Analysis and Probability Seminar

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Title: Densely defined non-closable curl on the Mackay-Tyson-Wildrick carpets
Speaker: Alexander Teplyaev (University of Connecticut)
Time: Friday, March 23, 2018 at 1:30 pm
Place: MONT 414Abstract: The talk will discuss the possibly degenerate behavior of the exterior derivative operator defined on 1-forms on metric measure spaces. The main examples we consider are the non self-similar Sierpinski carpets recently introduced by Mackay, Tyson and Wildrick. Although topologically one-dimensional, they have positive two-dimensional Lebesgue measure and carry nontrivial 2-forms. We prove that in this case the curl operator (and therefore also the exterior derivative on 1-forms) is not closable, and that its adjoint operator has a trivial domain. This is a joint work with Michael Hinz.

Organizer: Vasileios Chousionis and Oleksii Mostovyi