In progress:
 A deformation of Borel equivariant homotopy (with Gabriel AngeliniKnoll, Eva Belmont, and Hana Jia Kong). In progress.
Publications:
 The structure of the v_2local algebraic tmf resolution (with Prasit Bhattacharya and Dominic Culver). Submitted, last updated 1/26/23.
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 The 2primary Hurewicz image of tmf (with Mark Mahowald and J.D. Quigley). To appear in Geometry and Topology.
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 The telescope conjecture at height 2 and the tmf resolution (with Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu). J. Topology 14 (2021) 12431320.
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 C_2equivariant stable homotopy from real motivic stable homotopy (with Jay Shah). Annals of Ktheory 5 (2020) 411464.
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 The BousfieldKuhn functor and topological AndreQuillen cohomology
(with Charles Rezk). Inventiones 220 (2020) 9491022.
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 Detecting exotic spheres in low dimensions using coker J
(with Mike Hill, Mike Hopkins, and Mark Mahowald). J. London Math. Soc.101 (2020) 11731218.
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 On the E2term of the boAdams spectral sequence
(with Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu). J. Topology 13 (2020) 356415.
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 Topological modular and automorphic forms
Handbook of Homotopy Theory, edited by H.~Miller, Chapman and Hall/CRC Handbooks in Mathematics Series (2019).
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 On the ring of tmf cooperations at the prime 2
(with Kyle Ormsby, Nat Stapleton, and Vesna Stojanoska), Journal of Topology 12 (2019) 577657.
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 Spectral algebra models of unstable v_nperiodic homotopy theory
(with Charles Rezk). Springer Proc. in Math. and Stat. 309 (2019).
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 A C_2equivariant analog of Mahowald's Thom spectrum theorem
(with Dylan Wilson). Proceedings of the AMS 146 (2018), 50035012.
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 On the homotopy of Q(3) and Q(5) at the prime 2
(with Kyle Ormsby) Alg. Geom. Topol. 165 (2016), 24592534.
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 The construction of tmf
Topological Modular Forms, AMS Mathematical Surveys and Monographs 201 (2014) 131188.
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 The Goodwillie tower and the EHP sequence
Memoirs of the AMS. 1026 (2012) ixi, 190
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 The homotopy groups of the E(2)local sphere at p > 3,
revisited
Adv. Math. 230 (2012) 458492.
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 The Goodwillie tower for S^1 and Kuhn's theorem
Alg. Geom. Topol. 11 (2011), 24532475
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 Higher real Ktheories and topological automorphic forms
(with Mike Hopkins) J. Topology 4 (2011), 3972.
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 Topological automorphic forms on U(1,1)
(with Tyler Lawson) Math. Zeit. 267 (2011), 497522.
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 Topological automorphic forms
(with Tyler Lawson) Mem. Amer. Math. Soc. 958 (2010), ixxiii, 1132.
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 The homotopy fixed point spectra of profinite Galois
extensions
(with Daniel G. Davis) Trans. Amer. Math. Soc. 362 (2010) 49835042.
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 betafamily congruences and the finvariant
(with Gerd Laures) Geom. Topol. Monographs 16 (2009) 929.
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 Congruences between modular forms given by the divided beta family
in homotopy theory
Geometry and Topology 13 (2009) 319357.
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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) 4584.
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 Buildings, elliptic curves, and the K(2)local sphere
American Journal of Mathematics 129 (2007) 15131563.
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 Some root invariants at the prime 2
Geometry and Topology
Monographs 10 (2007), 140.
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Isogenies of elliptic curves and the Morava stabilizer group
(With Tyler Lawson)
Journal of Pure and Applied Algebra 207 (2006) 3749.
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 A modular description of the K(2)local sphere at the prime
3
Topology 45 (2006), 343402.
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 Root invariants in the Adams spectral sequence
Trans. Amer. Math. Soc. 358 (2006), 42794341
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On the existence of the self map v_2^9 on the
SmithToda complex V(1) at the prime 3
(With Satya Pemmaraju)
Contemp. Math. 346 (2004), 949.
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 Addendum to "A new proof of the Bott periodicity theorem"
Topology and its Applications 143 (2004), 281290.
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 A new proof of the Bott periodicity theorem
Topology and its Applications 119 (2002), 167183.
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