Categorical dynamics on stable module categories

Abstract: Given a mathematical object X and an endomorphism f of X, entropy assigns to this pair a number h(f) measuring the dynamical complexity of f. Initially defined for measure spaces and topological spaces, it has also been generalized by Dimitrov--Haiden--Katzarkov--Kontsevich to measure the complexity of endomorphisms of stable ∞-categories. I will discuss a result showing that the categorical polynomial entropy of a twist functor on stable module categories of certain algebras A of cohomology operations over a field k reflects the complexity of A: it is at least one less than the Krull dimension of H*(A;k), generalizing results of Fan--Fu--Ouchi. We will then discuss work in progress to bring this dynamicalperspective to homotopy theory.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

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