Topology Seminar: Jonathan Campbell
Topic
Cutting and Pasting in Algebraic K-theory -- AKA Combinatorial K-theory
Speakers
Details
Algebraic K-theory is an invariant defined on categories that records how object in the category are related by exact sequences --- it is a homotopical version of the classical Euler characteristic. However, there are many categories of interest that do not have exact sequences, but instead have cutting and pasting operations. For example, the category of varieties or the category of polytopes. I'll describe how to define a higher algebraic K-theory for categories like this, and show that it's not so different from the case of more algebraic categories. Even better, theorems like Quillen's Devissage and Localization can be proved internal to these structures. Time permitting, I'll describe how the cutting and pasting of polytopes is intimately related to the weight filtration on the algebraic K-theory of fields.
Additional Information
Location: ESB 4133 (PIMS Lounge)
Jonathan Campbell, Vanderbilt
Jonathan Campbell, Vanderbilt
This is a Past Event
Event Type
Scientific, Seminar
Date
November 14, 2018
Time
-
Location