Serre weights for wildly ramified three-dimensional representations (with Daniel Le, Bao V. Le Hung, Stefano Morra), in preparation.
Reductions of some two dimensional crystalline representations via Kisin modules (with John Bergdall), [pdf] .
Serre weights and Breuil's lattice conjecture in dimension three (with Daniel Le, Bao V. Le Hung, Stefano Morra), [pdf] .
Compatible systems of Galois representations associated to the exceptional group E6 (with G. Boxer, F. Calegari, M. Emerton, K. Madapusi Pera, S. Patrikis), to appear in Forum of Math, Sigma [pdf] .
A Harder-Narasimhan theory for Kisin modules (with Carl Wang Erickson), to appear in Alg. Geometry [slides] [pdf] .
Weight elimination in Serre-type conjectures (with Daniel Le, Bao V. Le Hung), to appear in Duke Math. J. [pdf] .
Moduli spaces of Kisin modules with descent data and parahoric local models (with Ana Caraiani) Ann. Sci. de l'ENS 51 (2018), no. 1, 181-213. [pdf] .
Potentially crystalline deformation rings and Serre weight conjectures (with D. Le, B. V. Le Hung, S. Morra) Inventiones Mathematicae 212 (2018), no. 1, 1-107. [summary] [pdf] .
Local models for Weil-restricted groups Compositio Mathematica 152 (2016), no. 12, 2563-2601. [pdf].
Potentially crystalline deformation rings in the ordinary case (with Stefano Morra) Annales de l'Institut Fourier 66 (2016), no. 5, 1923-1964. [pdf].
G-valued crystalline representations with minuscule p-adic Hodge type, Algebra & Number Theory 9 (2015), no. 8, 1741-1792. [pdf]
These notes were written for lectures I
gave as a graduate student at the number theory learning seminar at
Stanford. They fit in with larger series available
at the seminar pages listed. Nothing beyond the
presentation is original to these notes.