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

Sanath Devalapurkar (U Chicago): The J-homomorphism, Bott periodicity, and the Weil representation

Event Type: Seminar/Symposium
Sponsor: UIUC Math Department
Location: Altgeld 243
Date: Sep 9, 2025 11:00 am
Views: 130
Originating Calendar: Topology Seminar; Let V be a symplectic vector space, so that the symplectic group Sp(V) acts on V. If L is a Lagrangian subspace of V, and k is a commutative ring, then the k-module Map(L, k) is a “geometric quantization” of V. However, it does not admit an action of Sp(V); but there is a central extension of Sp(V) by the group k* of units in k, called the metaplectic group, which *does* act on Map(L, k). This is called the Weil representation, and it plays an important role in many areas of mathematics. I will explain a categorification of the Weil representation, where the metaplectic group is replaced by an extension of Sp(V) by the classifying space Bk*. I will also allow k to be a ring spectrum, and explain how the cocycle defining the extension of Sp(V) by Bk* is computed by the J-homomorphism. This is motivated by 1) applications to Langlands duality with coefficients in ring spectra (cf my thesis); 2) work of Teleman and Braverman-Dhillon-Finkelberg-Raskin-Travkin; and 3) Maslov data in Floer homotopy theory; I hope to explain these relationships in the talk.

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