Jack Shotton

A picture of me.

I am an L. E. Dickson Instructor in the Department of Mathematics at the University of Chicago. Previously I was a PhD student at Imperial College London under the supervision of Professor Toby Gee.

Here is my CV, my current research statement, and a short version of the latter.

My email address is jshotton@math.uchicago.edu.

I am co-organiser of the number theory seminar this year.

Research

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

Papers.

  1. 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.
    ArXiV version, Journal version.
  2. The Breuil-Mézard conjecture when l \neq p.
    To appear in Duke Mathematical Journal.
    ArXiV version.
  3. 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.
    Preprint 2017.
  4. On the category of finitely presented mod p representations of GL_2(F), F/Q_p finite.
    Preprint 2017.
  5. A local proof of the Breuil-Mézard conjecture when l \neq p.
    In preparation.
  6. New cases of Ihara's lemma for Shimura curves over Q. with Jeffrey Manning.
    In preparation.
My thesis essentially contains the first two papers above.

Teaching.

In Winter 2018 I am teaching 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.

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.