Time: 11:30
Speaker: Paul Baum (Penn State)
Title: "What is K-theory and what is it good for?"
Room: MC 106

Abstract: This talk will consist of four points:

1. The basic definition of K-theory
2. A brief history of K-theory
3. Algebraic versus topological K-theory
4. The unity of K-theory

The talk is intended for non-specialists, so the basic definitions will be carefully stated. It should also serve as an introduction to my next 3 lectures.

Time: 15:30
Speaker: Kyle Ormsby (Michigan)
Title: "The motivic alpha family over p-adic fields"
Room: MC 108

Abstract: Using a splitting of the algebraic Brown-Peterson spectrum (at the prime 2), I describe the E_2-term of the motivic Adams-Novikov spectral sequence over a p-adic field (p > 2) and identify an analogue of the alpha family within it. Inspired by classical computations from topology and previous work over algebraically closed fields, I determine the behavior of this family, discovering new phenomena (like the existence of nontrivial d_2-differentials) along the way. This produces an ``infinite result" in the stable motivic homotopy groups of the 2-complete sphere spectrum over p-adic fields.