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 jack.g.shotton@durham.ac.uk.

## 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.