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topology seminar

Topology Seminar

Categorical dynamics on stable module categories

Topological entropy is a measure of the complexity of a continuous self-map of a compact topological space. Categorical entropy generalizes this measure to exact endofunctors of triangulated categories. In this work we ask: How can categorical entropy serve to quantify growth in stable homotopy theory, and how can the methods of stable homotopy theory aid in understanding and computing categorical entropy? We show that the categorical polynomial entropy of a twist functor on the stable module category of a finite connected graded Hopf algebra A over a field k recovers one less than the Krull dimension of H*(A;k), generalizing a computation of Fan, Fu, and Ouchi. Along the way, we will see how a stable homotopy theoretic-perspective permits us to make this refinement.

Date:
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Location:
POT 745
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Topology Seminar

Factoring the Burnside Adams Operation through the Power Operation

Within representation theory, it's well known that the Adams operation can be factored through the power operation. Similar factorizations exist for some other cohomology theories. It is not known for the Burnside ring. Our primary goal is to describe such a factorization for the Burnside ring in certain cases. We begin by recalling the Burnside ring and these operations, then observing a theorem by Gay, Morris, and Morris which describes the Adams operation, and finally, describing the three major steps of the proof.

Date:
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Location:
POT 745
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Topology Seminar

During the semester, the UK Math Topology Seminar usually meets on Thursdays at 3:30 PM in POT 745. However, there are two exceptions for the SP2018: February 9 and April 10. On April 10, the seminar will meet between 3:00-6:00. Please visit UK Math Topology Seminar for updates and information about presenters. 

Date:
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Location:
POT 745
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