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

Here is
my CV.

My email address is jshotton@math.uchicago.edu.

I am co-organiser of the number theory seminar this year.

## 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.

ArXiV
version, Journal version.
- The Breuil-Mézard conjecture when l \neq p.

To appear in Duke Mathematical Journal.

ArXiV version.
- 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.

Preprint 2017.
- On the category of finitely presented mod p representations of GL_2(F), F/Q_p
finite.

Preprint 2017.
- A local proof of the Breuil-Mézard conjecture when l \neq p.

In preparation.
- New cases of Ihara's lemma for Shimura curves over Q. with Jeffrey Manning.

In preparation.

My

thesis essentially contains the first two papers above.

## Teaching.

In Winter 2018 I am teaching 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.