Accepted & Published Papers

Title & Description	MathRev	Paper
THH of \ell and ko (Joint with Angeltveit and Lawson) This paper simultaneously runs two pairs of Bockstein spectral sequences to compute topological Hochschild homology.	arXiv
The spectra ko and ku are not Thom spectra (Joint with Angeltveit and Lawson) Using Hochschild homology, we show that ko and ku are not Thom spectra.		arXiv
The String Bordism of BE_8 This computes the String Bordism groups of BE_8 and BE_8\times BE_8 through dimension 14. This computation amounts to computing the tmf-homology of K(Z,3).		arXiv
A v_2^32 self-map of M(1,4) at the prime 2 (Joint with Behrens, Hopkins, & Mahowald) This proves the existence of a v_2^32-self map on the generalized Smith-Toda complex M(1,4).	MR	arXiv
The 5-Local Homotopy of eo_4 A Bockstein and Adams-Novikov spectral sequence computation for the homotopy ring of the conjectural spectrum eo_4.	MR	arXiv
Cyclic comodules, the Homology of j and j-Homology An elementary presentation of the cohomology of the connective j-theory spectrum.	MR	PDF
The tmf-homology of BSigma_3 This gives a form of the Adams spectral sequence for tmf-homology and applies it to compute the tmf-homology of BSigma_3.	MR	PDF

Submitted Papers

Title & Description	Paper
Ext and the motivic Steenrod algebra over $\mathbb R$ This demonstrates a motivic Bockstein spectral sequence used to compute motivic Ext over finite subalgebras of the Motivic Steenrod algebra. (Updated 3/27/09).	arXiv
Automorphic forms and cohomology theories on Shimura curves of small discriminant (Joint with Lawson) We compute several rings of automorphic forms and apply this to compute the homotopy groups of several spectra produced by Lurie's Artin Representability.	arXiv
Homological obstructions to string orientations (Joint with Douglas and Henriques) This paper analyzes Poincare duality in the context of modules over the Steenrod algebra	arXiv

Preprints

Title & Description	Paper
On the non-existence of elements of Kervaire invariant one (Joint with Hopkins and Ravenel) In this paper, we prove that there are no smooth Kervaire invariant one manifolds of dimension larger than 126 using equivariant homotopy theory.	arXiv
The Homotopy of $EO_{2p-2}$ (Joint with Hopkins and Ravenel) This computation provides a complete, toy example demonstrating how to compute the homotopy of the higher real K-theories.	PDF
A Hopf algebra for Computing eo_{p-1} Homology This generalizes the computations done early for tmf at the prime 3 to the conjectural spectrum eo_{p-1} at the prime p.

Notes & Computations

Title & Description	Paper
Motivic THH(HF_p) and THH(HZ) Bokstedt spectral sequences motivically. There are several subtleties that differ wildly from the classical version, including surprising divisibility by p. (This is currently flawed and in progress).	PDF
Computation of Ext over Motivic A(2) at the prime 2 This repeats the computation for motivic homotopy over C.	PDF
Computation of Ext over A(2) at the prime 2 The May spectral sequence computation of Ext over A(2).	PDF

Back Burner Projects

Project & Summary	Last Update
The tmf-homology of tmf Using the Hopf algebroid described above computing tmf-homology at 3, it is easy to compute the mod 3 homology of tmf. This can then be used to mirror Mahowald's computations of a splitting of bo^bo and bo-resolutions.	2007
Differentials and Massey Products It is easy to show that 3-fold Massey products satisfy a kind of Leibnitz rule for higher differentials. Computational evidence shows that this is true in general, and this project's goal is to analyze this for a general DGA.	2007

Talks & Write-ups

Title	Date	File
On the slice filtration and the Kervaire invariant one problem This talk was given at p-adic geometry and homotopy theory at Loen, Norway. It includes some commentary about possible connections to algebraic K-theory.	August, 2009	Slides
On the Non-Existence of Manifolds of Kervaire Invariant One This talk was given at the Isle of Skye about the work with Hopkins and Ravenel.	June, 2009	Slides
On the Non-Existence of Manifolds of Kervaire Invariant One This was my talk at the Georgia topology conference the recent work with Hopkins and Ravenel on the Kervaire invariant.	May, 2009	Slides
Asymptotics in Homotopy Ramifications of recent work with Hopkins and Ravenel. UCSD Colloquium	November, 2008	Slides
Power Operations and Differentials in Higher Real $K$-Theory Discussion of techniques employed with Hopkins and Ravenel. AMS Special Session, Middleton, CT.	November, 2008	Slides
Computations towards $K(ko)$ Discussion of work with Angeltveit and Lawson about K(ko), integrally. AMS Special Session, Murphresboro, TN.	November, 2007	Slides
Computational work on $EO_n$ Survey of work with Hopkins and Ravenel presented at the Homotopy Workshop at Oberwolfach	September, 2007	MFO Report
The twisted $K$-homology of simple Lie groups Douglas' work on the twisted K-homology of simple Lie groups at the twisted K-theory Arbeitsgemeinschaft	October, 2006	MFO Report