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

Meng Guo (UIUC): Khovanov stable homotopy type

Event Type: Seminar/Symposium
Sponsor: UIUC math department
Location: Altgeld 241
Date: Nov 12, 2024 11:00 am
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Originating Calendar: Topology Seminar; Khovanov homology assigns a graded chain complex of vector spaces to a link or a tangle. The construction categorifies the Jones polynomial, by taking the Euler characteristic of the Khovanov homology. Lipshitz—Sarkar and Hu--Kriz—Kriz construct a spectrum associated to a link whose homology is Khovanov homology and these constructions are proved to be equivalent by Lawson--Lipshitz—Sarkar. Spectra associated to tangles are later constructed by Lawson--Lipshitz—Sarkar. On the other hand, there is a sign discrepancy of Khovanov homology that two movies representing equivalent cobordisms induce homotopy equivalent chain maps only up to sign. In this talk, I will give an overview of this subject and describe an ongoing work on how to fix the sign on the spectrum level. This is an ongoing joint work by Anne Dranowski, Aaron Lauda, and Andrew Manion.

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