Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Andres Mejia (U Penn): An Equivariant Calculus of Embeddings

Event Type: Seminar/Symposium
Sponsor: UIUC Math Department
Location: Altgeld 241
Date: Nov 5, 2024 11:00 am
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Originating Calendar: Topology Seminar; A classical problem in manifold topology is to understand when two given embeddings are isotopic. The desire to understand when such isotopies are unique leads one to instead consider the space of embeddings between two smooth manifolds. Goodwillie and Weiss provide an approach by trying to study the values of embeddings in small neighborhoods of configuration spaces for a manifold. We extend these methods to the setting of manifolds with an action by a finite group. In particular, we study the space of equivariant embeddings by scanning along an appropriate notion of $G$-disks. Leveraging the work of Bierstone in equivariant immersion theory, we show that the first approximation to equivariant embeddings is the space of equivariant immersions. Moreover, we show that the layers of our embedding tower can be analyzed as fibrations over a product of nonequivariant configuration spaces.

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