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## Jack Shotton

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.

Here is my CV.

My email address is [email protected].

### 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.

pdf, journal.

There is an error in the proof of Proposition 2.7 that is corrected in the pdf version here.*The Breuil-Mézard conjecture when l \neq p.*

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

pdf, journal.*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.

Mathematische Annalen 373 (2019), 421-487

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

Documenta Mathematica 25 (2020), 143-157

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

with Jeffrey Manning.

To appear in Mathematische Annalen.

pdf*Generic local deformation rings when l \neq p.*

Preprint.

pdf

My thesis essentially contains the first two papers above.

### Teaching at Durham.

In 2020-2021 I am teaching Representation Theory III/IV, which I also taught in 2019-2020.

In Michaelmas 2018 I taught MATH3401, Cryptography and Codes III.

### Teaching at Chicago.

In Winter 2018 I taught 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.