- The Hurewicz image of tmf (with Mark Mahowald and J.D. Quigley) We compute the Hurewicz image of tmf.
- On the tmf-resolution of Z (with Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu). Last updated 9/29/19. Submitted.
- C_2 equivariant homotopy groups from real motivic homotopy groups (with Jay Shah). To appear in Annals of K-theory.
- The Bousfield-Kuhn functor and topological Andre-Quillen cohomology
(with Charles Rezk). Inventiones 220 (2020) 949-1022.
- Detecting exotic spheres in low dimensions using coker J
(with Mike Hill, Mike Hopkins, and Mark Mahowald). J. London Math. Soc.101 (2020) 1173-1218.
- On the E2-term of the bo-Adams spectral sequence
(with Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu). J. Topology 13 (2020) 356-415.
- Topological modular and automorphic forms
Handbook of Homotopy Theory, edited by H.~Miller, Chapman and Hall/CRC Handbooks in Mathematics Series (2019).
- On the ring of tmf cooperations at the prime 2
(with Kyle Ormsby, Nat Stapleton, and Vesna Stojanoska), Journal of Topology 12 (2019) 577-657.
- Spectral algebra models of unstable v_n-periodic homotopy theory
(with Charles Rezk). Springer Proc. in Math. and Stat. 309 (2019).
- A C_2-equivariant analog of Mahowald's Thom spectrum theorem
(with Dylan Wilson). Proceedings of the AMS 146 (2018), 5003-5012.
- On the homotopy of Q(3) and Q(5) at the prime 2
(with Kyle Ormsby) Alg. Geom. Topol. 16-5 (2016), 2459-2534.
- The construction of tmf
Topological Modular Forms, AMS Mathematical Surveys and Monographs 201 (2014) 131-188.
- The Goodwillie tower and the EHP sequence
Memoirs of the AMS. 1026 (2012) i-xi, 1-90
- The homotopy groups of the E(2)-local sphere at p > 3,
Adv. Math. 230 (2012) 458-492.
- The Goodwillie tower for S^1 and Kuhn's theorem
Alg. Geom. Topol. 11 (2011), 2453-2475
- Higher real K-theories and topological automorphic forms
(with Mike Hopkins) J. Topology 4 (2011), 39-72.
- Topological automorphic forms on U(1,1)
(with Tyler Lawson) Math. Zeit. 267 (2011), 497-522.
- Topological automorphic forms
(with Tyler Lawson) Mem. Amer. Math. Soc. 958 (2010), i-xxiii, 1-132.
- The homotopy fixed point spectra of profinite Galois
(with Daniel G. Davis) Trans. Amer. Math. Soc. 362 (2010) 4983-5042.
- beta-family congruences and the f-invariant
(with Gerd Laures) Geom. Topol. Monographs 16 (2009) 9-29.
- Congruences between modular forms given by the divided beta family
in homotopy theory
Geometry and Topology 13 (2009) 319-357.
- On the existence of a v_2^32 self map on M(1,4) at the prime
(With Mike Hill, Mike Hopkins, and Mark Mahowald)
Homology, Homotopy, and Applications 10 (2008) 45-84.
- Buildings, elliptic curves, and the K(2)-local sphere
American Journal of Mathematics 129 (2007) 1513-1563.
- Some root invariants at the prime 2
Geometry and Topology
Monographs 10 (2007), 1-40.
Isogenies of elliptic curves and the Morava stabilizer group
(With Tyler Lawson)
Journal of Pure and Applied Algebra 207 (2006) 37-49.
- A modular description of the K(2)-local sphere at the prime
Topology 45 (2006), 343-402.
- Root invariants in the Adams spectral sequence
Trans. Amer. Math. Soc. 358 (2006), 4279-4341
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.
- Addendum to "A new proof of the Bott periodicity theorem"
Topology and its Applications 143 (2004), 281-290.
- A new proof of the Bott periodicity theorem
Topology and its Applications 119 (2002), 167-183.