Jack Shotton

I am an Assistant Professor in the Department of Mathematical Sciences at Durham University.

Previously I was an L. E. Dickson Instructor in the Department of Mathematics at the University of Chicago and a PhD student at Imperial College London under the supervision of Professor Toby Gee.

Here is my CV.

My email address is [email protected].

Research

I am interested in number theory, especially in Galois representations and arithmetic properties of automorphic forms.

Papers.

Local deformation rings for GL_2 and a Breuil-Mézard conjecture when l \neq p.
Algebra and Number Theory 10 (2016), no. 7, 1437-1475.
pdf, journal.
There is an error in the proof of Proposition 2.7 that is corrected in the pdf version here.
The Breuil-Mézard conjecture when l \neq p.
Duke Math. Journal 167 (2018), no. 4, 603-678.
pdf, journal.
Local deformation rings for 2-adic deformation rings of G_{Q_l}, l \neq 2.
Appendix to On crystabeline deformation rings of Gal(\bar{Q_p}/Q_p) by Yongquan Hu and Vytautas Paškūnas.
Mathematische Annalen 373 (2019), 421-487
pdf, journal.
The category of finitely presented mod p representations of GL_2(F).
Documenta Mathematica 25 (2020), 143-157
pdf, journal
Ihara’s lemma for Shimura curves over totally real fields via patching.
with Jeffrey Manning.
To appear in Mathematische Annalen.
pdf
Generic local deformation rings when l \neq p.
Preprint.
pdf

My thesis essentially contains the first two papers above.

Teaching at Durham.

In 2020-2021 I am teaching Representation Theory III/IV, which I also taught in 2019-2020.
In Michaelmas 2018 I taught MATH3401, Cryptography and Codes III.

Teaching at Chicago.

In Winter 2018 I taught Math 258, Honors Basic Algebra 2. The course material is on Canvas.
In Autumn 2017 I taught Math 257, Honors Basic Algebra 1.
In Spring 2017 I taught Math 163, Honors Calculus 3.
In Winter 2017 I taught Math 162, Honors Calculus 2.
In Autumn 2016 I taught Math 161, Honors Calculus 1.
In Spring 2016 I taught two sections of Math 159, introduction to proof in analysis and linear algebra. Course pages: section 41 and section 57.
In Autumn 2015 and Winter 2016 I taught Math 159, introduction to proof in analysis and linear algebra.

In summer 2017, I supervised a reading project for David Lin. His writeup, which among other things contains a proof of the Kronecker-Weber theorem for cubic extensions, can be found here.

Other

I was the organiser for a TCC event day in number theory held on April 13th 2015 at Imperial College, London. The event page is here.