Jack Shotton

About 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.

Research

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

Papers.

1. Irreducible components of the moduli space of Langlands parameters.
   Submitted.
   pdf
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.

PhD Students

• Daniel Funck 2018-2023 (expected).

Undergraduate summer students

• 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.

• 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.