Jack Shotton

About me

A picture of me.

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.

My email address is jack.g.shotton@durham.ac.uk.


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


  1. Irreducible components of the moduli space of Langlands parameters.
  2. On endomorphism algebras of Gelfand--Graev representations II.
    with Tzu-Jan Li
    To appear in Bulletin of the London Mathematical Society
    pdf, journal.
  3. Generic local deformation rings when \(l \neq p\).
    Compositio Mathematica, 158(4), 721-749 (2022).
    pdf, journal.
  4. Ihara's lemma for Shimura curves over totally real fields via patching.
    with Jeffrey Manning.
    Mathematische Annalen 379, 187-234 (2021).
    pdf, journal.
  5. The category of finitely presented mod p representations of \(GL_2(F)\).
    Documenta Mathematica 25 (2020), 143-157
    pdf, journal
  6. Local deformation rings for 2-adic deformation rings of \(G_{\mathbb{Q}_l}\), \(l \neq 2\).
    Appendix to On crystabeline deformation rings of \(\mathrm{Gal}(\bar{\mathbb{Q}_p}/\mathbb{Q}_p)\) by Yongquan Hu and Vytautas Paškūnas.
    Mathematische Annalen 373 (2019), 421-487
    pdf, journal.
  7. The Breuil-Mézard conjecture when \(l \neq p\).
    Duke Mathematical Journal 167 (2018), no. 4, 603-678.
    pdf, journal.
  8. 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.
My thesis essentially contains the last two papers above.

PhD Students

Undergraduate summer students


In 2023-2024 I will be offering two projects: Cyclotomic Polynomials at level III and Elliptic Curves at level IV.

Before coming to Durham I taught Introduction to Proof in Analysis and Linear Algebra, Honors Calculus, and Honors Basic Algebra at the University of Chicago.