Brandon W. Levin

Assistant Professor, University of Arizona

Office: ENR2 S339

Email: bwlevin [at] math [dot] arizona [dot] edu

You can find my CV here.

Research interests:

Integral p-adic Hodge theory
Galois deformations/modularity lifting
Local models of Shimura varieties
Geometry of affine flag varieties

Publications/Preprints:

G-valued crystalline deformation rings in the Fontaine-Laffaille range (with J. Booher), [pdf] .

Local models for Galois deformation rings and applications (with Daniel Le, Bao V. Le Hung, Stefano Morra), [pdf] .

Reduction of 2-dimensional semistable representations with large L-invariant (with John Bergdall, Tong Liu), [pdf] .

Reductions of some two-dimensional crystalline representations via Kisin modules (with John Bergdall), to appear in IMRN [pdf] .

A Harder-Narasimhan theory for Kisin modules (with Carl Wang Erickson), Alg. Geometry 7 (2020), no. 6, 645-695 [slides] [pdf] .

Serre weights and Breuil's lattice conjecture in dimension three (with Daniel Le, Bao V. Le Hung, Stefano Morra), Forum of Math, Pi 8 (2020), e5, 135p. [pdf] .

Compatible systems of Galois representations associated to the exceptional group E6 (with G. Boxer, F. Calegari, M. Emerton, K. Madapusi Pera, S. Patrikis), Forum of Math, Sigma 7 (2019), e4, 29p. [pdf] .

Weight elimination in Serre-type conjectures (with Daniel Le, Bao V. Le Hung), Duke Math. J. 168 (2019), no. 13, 2433-2506 [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]

Teaching:

University of Arizona

Fall 2018: Linear Algebra (Math 513)
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).

Summers 2005-2008: Counselor at PROMYS.

Expository Notes:

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.

Schlessinger's criterion and deformation conditions (from the 2009-10 modularity lifting seminar)
Notes on Tate's article on p-divisible groups (this is part II of a series from the 2010-11 Mordell seminar)
Tate conjecture for abelian varieties over number fields (from the 2010-11 Mordell seminar)