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

Patching and the p-adic Langlands program for GL(2,ℚp) (with Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paškūnas, and Sug Woo Shin), arXiv:1609.06902. Submitted.
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On the generic part of the cohomology of compact unitary Shimura varieties (with Peter Scholze), arXiv:1511.02418. Submitted.
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Kisin modules with descent data and parahoric local models (with Brandon Levin), arXiv:1510.07503. To appear in Ann. Sci. École Norm. Sup.
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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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Conference proceedings:

p-adic q-expansion principles on unitary Shimura varieties (with Ellen Eischen, Jessica Fintzen, Elena Mantovan, and Ila Varma), arXiv:1411.4350. To appear in Directions in Number Theory: Proceedings of the WIN3 Workshop.
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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.
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Undergraduate papers:

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