Publications and preprints (click on title to view abstract):

Potential automorphy over CM fields (with Patrick B. Allen, Frank Calegari, Toby Gee, David Helm, Bao V. Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack A. Thorne)
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Perfectoid Shimura varieties, to appear in Perfectoid spaces: Lectures from the 2017 Arizona Winter School.
PDF Video
Shimura varieties at level Γ1(p) and Galois representations (with Daniel R. Gulotta, Chi-Yun Hsu, Christian Johansson, Lucia Mocz, Emanuel Reinecke, and Sheng-Chi Shih), arXiv:1804.00136.
PDF arXiv Video
Patching and the p-adic Langlands program for GL(2,ℚp) (with Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paškūnas, and Sug Woo Shin), Compositio Math. 154 (2018), no. 3, 503–548.
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Kisin modules with descent data and parahoric local models (with Brandon Levin), Ann. Sci. Éc. Norm. Supér. (4) 51 (2018), no. 1, 181–213.
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On the generic part of the cohomology of compact unitary Shimura varieties (with Peter Scholze), Annals of Math. 186 (2017), no. 3, 649–766.
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p-adic q-expansion principles on unitary Shimura varieties (with Ellen Eischen, Jessica Fintzen, Elena Mantovan, and Ila Varma), Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop. Springer International Publishing (2016), 197–243.
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On the image of complex conjugation in certain Galois representations (with Bao V. Le Hung), Compositio Math. 152 (2016), no. 7, 1476–1488.
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Patching and the p-adic local Langlands correspondence (with Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paškūnas, and Sug Woo Shin), Cambridge Journal of Math. 4 (2016), no. 2, 197–287.
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Monodromy and local-global compatibility for l=p, Algebra Number Theory 8 (2014), no. 7, 1597–1646.
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Local-global compatibility and the action of monodromy on nearby cycles, Duke Math. J. 161 (2012), no. 12, 2311–2413.
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Oberwolfach reports:

Patching and p-adic local Langlands, in Algebraische Zahlentheorie, joint with M. Emerton, T. Gee, D. Geraghty, V. Paškūnas, and S.W. Shin, Oberwolfach Report No. 32 (2014), 31–33.

Undergraduate papers:

Multiplicative semigroups related to the 3x+1 problem, Adv. Appl. Math. 45 (2010), no. 3, 373–389. PDF Journal