Current Courses

Math 227B - Algebraic Topology III

Spring 2019

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

Math 19 - Patterns and Symmetry in Art and Nature

Spring 2019

Talks & Write-ups

Namboodiri Lectures: Evenness in Algebraic Topology

Talk 3 Talk 2 Talk 1

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

On the Non-existence of elements of Kervaire invariant one

PDF

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

G-Symmetric Monoidal Categories and Commutative Algebras

PDF

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.

Localizations of Equivariant Commutative Ring Spectra

MFO Report

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.

The slice filtration

Video

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.