Time and date: 15 February 2023 at 2:00 pm | Location: Abacws 1.04 | Speaker: Sam Richardson
In this talk I will be your guide through the wonderful world of category theory, cohomology theories, and characteristic classes. My research has been focused on a certain map of spaces called the Weyl map which can be defined for any Lie group as it is dependent on something known as a maximal torus but we will deal only with the family of special unitary groups, and how it is transformed by composition with a map derived from exponential functors, functors from the category of isomorphism classes of vector spaces to itself that turn the direct sum into the tensor product, hence the name.
From any strict symmetric monoidal category (examples of which include the skeleton of the source and target categories of an exponential functor) one may construct a cohomology theory. Both of our categories result in cohomology theories that are closely related to K-theory where we can decompose the class of the Weyl map into easy to digest chunks, and then we can use a certain characteristic class to build natural transformations of cohomology theories that take our exotic cohomology theories back into the far more manageable ordinary cohomology with rational coefficients.
Bonus Round: An introductory talk on an important result in homological algebra. Short exact sequences induce long exact sequences of homology groups via two applications of the Snake Lemma.
