Abstracts for MPIM Topology Seminar

The goal of this talk is to describe the Anderson self-duality of the spectrum of topological modular forms, as well as the guiding analogous example of real K-theory. The results as well as some of the proofs will have the algebro-geometric flavor of Serre-Grothendieck duality.
The first part of my talk will consist of introductory material that could be summarized as "Tmf for the working algebraic topologist."

Morava E-theory is a cohomology theory with many amazing properties. During the first half of this talk we will introduce Morava E-theory and give an overview of its most important properties. During the second half of this talk we will discuss the relationship between the Morava E-theory of finite groups and algebraic geometry.

The Johnson filtration of the mapping class group gives rise to an associated graded Lie algebra. The higher order Johnson homomorphism embeds this Lie algebra in the larger but better understood Lie algebra of symplectic derivations. It has long been known that this is not surjective, and various families of obstructions to surjectivity have been constructed by several authors. We give a graph homology construction that unifies and expands all of the previously known obstructions (with one exception, the so-called Galois obstruction.)

In this talk, we will give an overview of some of the key concepts in chromatic homotopy theory. The goal is to explain how the chromatic point of view organizes the stable homotopy category.