Jack Shotton

About me

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

My research is currently supported by an EPSRC New Investigator Award (UKRI1020), which funds a postdoctoral position for Johannes Girsch (2025–2027).

Papers

1. (with Alexander Milner) The smallest invariant factor of elliptic curves, and coincidences.
   preprint
   pdf, arXiv.
2. (with Daniel Funck) Singularities of Steinberg deformation rings.
   Forum of Mathematics, Sigma, 14, e97 (2026)
   pdf, journal.
3. Irreducible components of the moduli space of Langlands parameters.
   International Mathematical Research Notices, 2024(11), 9020-9035 (2024)
   pdf, journal.
4. (with Tzu-Jan Li) On endomorphism algebras of Gelfand--Graev representations II.
   Bulletin of the London Mathematical Society, 55(6), 2876-2890 (2023)
   pdf, journal.
5. Generic local deformation rings when \(l \neq p\).
   Compositio Mathematica, 158(4), 721-749 (2022).
   pdf, journal.
6. (with Jeffrey Manning) Ihara's lemma for Shimura curves over totally real fields via patching.
   Mathematische Annalen 379, 187-234 (2021).
   pdf, journal.
7. The category of finitely presented mod p representations of \(GL_2(F)\).
   Documenta Mathematica 25 (2020), 143-157
   pdf, journal
8. 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.
9. The Breuil-Mézard conjecture when \(l \neq p\).
   Duke Mathematical Journal 167 (2018), no. 4, 603-678.
   pdf, journal.
10. 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.

Students

PhD Students

• Patrick Creagh (2024 - )
• Daniel Funck (2018-2023), "The geometry of unipotent deformation rings and applications (GOUDA)".

Undergraduate summer students

• Oliver Davies (2026).
• Alex Milner (2023), "Invariant factors of elliptic curves", funded by the LMS.
• Patrick Creagh (2022), "Steinitz classes of CM elliptic curves".
• Dylan Johnston (2019), "Positivity and the weight part of Serre's conjecture", funded by the LMS.
• David Lin (2017), "The Kronecker-Weber theorem"

Teaching

• 2025-2026: Representation Theory IV (Epiphany).
• 2024-2025: Cryptography and Codes III (Michaelmas).
• 2023-2024: Cryptography and Codes III (Michaelmas), Number Theory III (Epiphany).
• 2019-2023: Representation Theory IV. Lecture notes.
• 2018-2019: Cryptography and Codes III (Michaelmas).

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.