William Balderrama, University of Virginia

Thursday, November 16, 2023 - 3:30pm to 4:30pm

PDL C-401

Chromatic homotopy theory is an approach to understanding the stable homotopy groups of spheres, and stable homotopy theory in general, which filters the stable category by a form of complexity called "height". The height 1 portion of the sphere spectrum corresponds to what is seen by topological K-theory, through the J-homomorphism and the Hurewicz image of KO. Higher height phenomena is detected by certain generalizations of K-theory, namely the Morava E-theories and their fixed points.

I will talk about some of my work importing pieces of this story to the setting of equivariant stable homotopy theory. In particular, I will describe some computations and applications of equivariant K-theory and higher chromatic analogues.

**There will be a pre-talk aimed at graduate students 2:30-3:20 in PDL C-401.**