Morse-theoretic Gaussian Elimination

Morse-theoretic Gaussian Elimination

MSI Colloquium, where the school comes together for afternoon tea before one speaker gives an accessible talk on their subject

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Date/time
16 May 2024 4:00pm - 16 May 2024 5:00pm
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Speakers

Leonardo Maltoni (ANU)
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Description

Abstract

Someone told me once that Gaussian elimination is the one thing a mathematician learns as an undergrad and then never really uses in research. This talk is about proving this is false. I will first introduce a homological algebra version of Gaussian elimination, due to Bar-Natan, which can be used to simplify complexes (e.g., chain complexes) arising in many areas of mathematics such as algebraic topology and representation theory. Then, following Sk├Âldberg, I will explain how to interpret this operation as a "collapse" in the sense of Forman's discrete Morse theory. Finally I will describe an application of this method to Rouquier complexes, certain interesting objects upgrading the braid group to a category.

Location

Room 1.33 (Seminar Room), Hanna Neumann Building 145, Science Road, ANU

-35.275389387895, 149.11926090717

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