# Math 227B - Algebraic Topology III

## Spring 2019

This is the third quarter in algebraic topology, focusing on generalized cohomology theories and foundational papers.

This is the third quarter in algebraic topology, focusing on generalized cohomology theories and foundational papers.

I gave the 2017 Namboodiri Lectures at the University of Chicago.

- Grassmanians, Thom spectra, and Wilson spaces: classical constructions and $C_2$-equivariant analogs
- Extending to larger groups: the norm, $G$-equivariant Wilson spaces, and the equivariant Steenrod algebra
- Towards $RO(G)$-graded algebraic geometry: explorations of duality for Galois covers via equivariant homotopy

This is my ICM talk on my solution with Hopkins and Ravenel to the Kervaire invariant one problem.

This talk is about the evolving notion of a G-symmetric monoidal ctegory. basic properties are discussed, grounded in genuine equivariant spectra. At the end, several algebraic examples are presented.

This talk discusses joint work with Hopkins on localization of commutative rings. In particular, it sketches the proof of when localization preserves commutative ring objects in spectra.

This talk is my discussion of the slice filtration and its generalizations at the Hot Topics workshop for the Kervaire Invariant One problem at MSRI.