In progress:

• The Hurewicz image of tmf
  (with Mark Mahowald) We completely determine the image of the Hurewicz homomorphism for tmf.
• Topological modular forms of level 5
  (with Kyle Ormsby) We perform computations in the spectrum Q(5). We also revisit and extend some computations in Q(3) studied by Mahowald and Rezk.

Preprints:

• The Bousfield-Kuhn functor and topological Andre-Quillen cohomology
  (with Charles Rezk). We show that there is a natural transformation from the Bousfield-Kuhn functor to topological Andre-Quillen cohomology, which is an equivalence on spheres. This allows us to compute the E-homology of the v_n-periodic Goodwillie tower of the identity on odd spheres. draft

Publications:

• The Goodwillie tower for S^1 and Kuhn's theorem
  Alg. Geom. Topol. 11 (2011), 2453-2475
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• The Goodwillie tower and the EHP sequence
  103 pages, to appear in Memoirs of the AMS. (updated 4/7/11)
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• The homotopy groups of the E(2)-local sphere at p > 3, revisited
  Adv. Math. 230 (2012) 458-492.
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• Higher real K-theories and topological automorphic forms
  (with Mike Hopkins) J. Topology 4 (2011), 39-72.
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• Topological automorphic forms on U(1,1)
  (with Tyler Lawson) Math. Zeit. 267 (2011), 497-522.
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• beta-family congruences and the f-invariant
  (with Gerd Laures) Geom. Topol. Monographs 16 (2009) 9-29.
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• The homotopy fixed point spectra of profinite Galois extensions
  (with Daniel G. Davis) Trans. Amer. Math. Soc. 362 (2010) 4983-5042.
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• Congruences between modular forms given by the divided beta family in homotopy theory
  Geometry and Topology 13 (2009) 319-357.
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• Notes on the contruction of tmf
  To appear in proceedings of 2007 Talbot Workshop. (revised: 11/16/11)
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• 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.
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• Topological automorphic forms
  (with Tyler Lawson) Mem. Amer. Math. Soc. 958 (2010), i-xxiii, 1-132.
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• Buildings, elliptic curves, and the K(2)-local sphere
  American Journal of Mathematics 129 (2007) 1513-1563.
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• Isogenies of elliptic curves and the Morava stabilizer group
  (With Tyler Lawson) Journal of Pure and Applied Algebra 207 (2006) 37-49.
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• Some root invariants at the prime 2
  Geometry and Topology Monographs 10 (2007), 1-40.
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• A modular description of the K(2)-local sphere at the prime 3
  Topology 45 (2006), 343-402.
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• Root invariants in the Adams spectral sequence
  Trans. Amer. Math. Soc. 358 (2006), 4279-4341
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• 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.
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• A new proof of the Bott periodicity theorem
  Topology and its Applications 119 (2002), 167-183.
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• Addendum to "A new proof of the Bott periodicity theorem"
  Topology and its Applications 143 (2004), 281-290.
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