Serre weights for wildly ramified three-dimensional representations (with Daniel Le, Bao V. Le Hung, Stefano Morra), in preparation.
Compatible systems of Galois representations associated to the exceptional group E6 (with George Boxer, Frank Calegari, Matthew Emerton, Keerthi Madapusi Pera, Stefan Patrikis), [pdf] .
Weight elimination in Serre-type conjectures (with Daniel Le, Bao V. Le Hung), [pdf] .
Serre weights and Breuil's lattice conjecture in dimension three (with Daniel Le, Bao V. Le Hung, Stefano Morra), [pdf] .
A Harder-Narasimhan theory for Kisin modules (with Carl Wang Erickson) [slides] [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 Daniel Le, Bao V. Le Hung, Stefano 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]
Teaching:
University of Arizona
Spring 2018: Calculus 2 (Math 129)
Fall 2017: Calculus 1 (Math 125)
University of Chicago
2015 - 2016: Honors Calculus (Math 161-163).
Spring 2015: Analysis (Math 203).
Winter 2015: Linear algebra with applications (Math 196).
Fall 2014: Elementary Number Theory (Math 175).
Stanford University
Fall 2010: TA for Linear algebra and Multivariable
calculus (Math 51).
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.