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.

- Irreducible components of the moduli space of Langlands parameters.

Submitted.

pdf - On endomorphism algebras of Gelfand--Graev representations II.

with Tzu-Jan Li

To appear in Bulletin of the London Mathematical Society

pdf, journal. - Generic local deformation rings when \(l \neq p\).

Compositio Mathematica, 158(4), 721-749 (2022).

pdf, journal. - Ihara's lemma for Shimura curves over totally real fields via patching.

with Jeffrey Manning.

Mathematische Annalen 379, 187-234 (2021).

pdf, journal. - The category of finitely presented mod p representations of \(GL_2(F)\).

Documenta Mathematica 25 (2020), 143-157

pdf, journal - 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. - The Breuil-Mézard conjecture when \(l \neq p\).

Duke Mathematical Journal 167 (2018), no. 4, 603-678.

pdf, journal. - 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.

- Daniel Funck 2018-2023 (expected).

- 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"

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

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.