Publications:

Higher real K-theories and topological automorphic forms
(with Mike Hopkins) Submitted.
pdf
Topological automorphic forms on U(1,1)
(with Tyler Lawson) To appear in Math. Zeit.
pdf (revised 10/4/09)
beta-family congruences and the f-invariant
(with Gerd Laures) To appear in Geometry and Topology Monographs.
pdf (revised 11/14/08)
The homotopy fixed point spectra of profinite Galois extensions
(with Daniel G. Davis) To appear in Transactions of the AMS.
pdf (revised 7/5/09)
Congruences between modular forms given by the divided beta family in homotopy theory
Geometry and Topology 13 (2009) 319-357.
pdf
Notes on the contruction of tmf
This is a writeup of the material behind a talk I gave on the subject at the 2007 Talbot Workshop. This is an expository article. Last updated 12/12/07.
pdf
On the existence of a v_2^32 self map on M(1,4) at the prime 2
(With Mike Hill, Mike Hopkins, and Mark Mahowald) Homology, Homotopy, and Applications 10 (2008) 45-84.
pdf
Topological automorphic forms
To appear in Memoirs of the AMS.
pdf (revised 9/16/08)
Buildings, elliptic curves, and the K(2)-local sphere
American Journal of Mathematics 129 (2007) 1513-1563.
pdf
Isogenies of elliptic curves and the Morava stabilizer group
(With Tyler Lawson) Journal of Pure and Applied Algebra 207 (2006) 37-49.
pdf
Some root invariants at the prime 2
Geometry and Topology Monographs 10 (2007), 1-40.
pdf
A modular description of the K(2)-local sphere at the prime 3
Topology 45 (2006), 343-402.
pdf
Root invariants in the Adams spectral sequence
Trans. Amer. Math. Soc. 358 (2006), 4279-4341
pdf
On the existence of the self map v_2^9 on the Smith-Toda complex V(1) at the prime 3
(With Satya Pemmaraju) Contemp. Math. 346 (2004), 9-49.
pdf
A new proof of the Bott periodicity theorem
Topology and its Applications 119 (2002), 167-183.
pdf
Addendum to "A new proof of the Bott periodicity theorem"
Topology and its Applications 143 (2004), 281-290.
pdf

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