Forum for invited speakers giving mathematical colloquium talks.
Chris Manon (GMU) - TBA
Mona Merling (JHU) - Equivariant algebraic K-theory
The first definitions of equivariant algebraic K-theory were given in the early 1980’s by Fiedorowicz, Hauschild and May, and by Dress and Kuku; however these early space-level definitions only allowed trivial action on the input ring or category. Equivariant infinite loop space theory allows us to define spectrum level generalizations of the early definitions: we can encode a G-action (not necessarily trivial) on the input as a genuine G-spectrum.
I will discuss some of the subtleties involved in turning a ring or space with G-action into the right input for equivariant algebraic K-theory or A-theory, and some of the properties of the resulting equivariant algebraic K-theory G-spectrum. For example, our construction recovers as particular cases equivariant topological real and complex K-theory, Atiyah’s Real K-theory and statements previously formulated in terms of naive G-spectra for Galois extensions.
I will also briefly discuss recent developments in equivariant infinite loop space theory from joint work with Guillou, May and Osorno (e.g., multiplicative structures) that should have long-range applications to equivariant algebraic K-theory.Add to Google Calendar
No seminar - Spring break
No Seminar - Spring Break