About me
As of July 1st 2024, I will be an Assistant Professor at Saint Mary's University.
I am a postdoc at the University of Colorado Boulder with mentor Katherine E. Stange.
I received my PhD in 2021 at McGill University under the supervision of Henri Darmon. My PhD studies were supported by a Vanier Canada Graduate Scholarship.
I was a Blyth Scholar during my undergraduate at Trinity College, Cambridge, where I received a BA(hons), MMath, and MA.
In high school I represented Canada at the 2011 and 2012 International Mathematical Olympiad, winning two silver medals.
I returned to the IMO as Observer B (2015), Leader (2017, 2018), and Observer A (2019). Since September 2019 I have been chair of the Canadian IMO Committee.
CV
ORCID
Research interests
I am interested in algebraic number theory, with an empahsis on computations, visualizations, and implementing algorithms. I write a large amount of code, mostly in PARI/GP and C, which can be found on my Github. Most of my current research falls under one or more of the following umbrellas:
- thin (semi-)groups, including Apollonian circle packings;
- arithmetic Fuchsian/Kleinian groups, especially their fundamental domains and geodesics;
- (indefinite) quadratic forms and (indefinite) quaternion algebras.
Updates
- 4 April 2024: Talk at IAS/Princeton Number Theory Seminar.
- 27 March 2024: Talk at Dalhousie University Number Theory Seminar.
- 25 March 2024: Colloquium talk at Dalhousie University.
- 5 - 9 February 2024: Attended Workshop: Shimura curves in the LMFDB at Dartmouth College.
- 30 January 2024: Colloquium talk at Saint Mary's University.
- 3 January 2024: New paper posted! Katherine E. Stange and I found reciprocity obstructions in a new setting: subsemigroups of SL(2, Z). We also disprove a conjecture of Bourgain and Kontorovich about a generalization of Zaremba's conjecture.
- 21 - 28 November 2023: Research visit to KIAS, South Korea.
- 1 November 2023: Contributed quotes to Quanta magazine article on quadratic reciprocity.
- 31 October 2023: Talk at the Penn State Number Theory Seminar.
- 10 October 2023: Talk at the University of Washington (Seattle) Number Theory Seminar.
- 11 - 15 September 2023: Attended Renormalization, computation and visualization in Geometry, Number Theory and Dynamics at CIRM, and gave a talk: "The not so local-global conjecture".
- 21 - 25 August 2023: Attended Isogeny Graphs in Cryptography at BIRS.
- 10 August 2023: Article published in Quanta magazine!
- 5 August 2023: New website is live!
- 3 August 2023: Talk in the Arithmetic Reflection Groups online seminar.
- 10 - 14 July 2023: Attended LMFDB Conference.
- 6 July 2023: Posted The Local-Global Conjecture for Apollonian circle packings is false.
- 2 - 13 July 2023: Canadian IMO team places 5th overall!
Contact
Department of Mathematics
University of Colorado Boulder
2300 Colorado Avenue
Boulder, CO 80309-0395
USA
Office: 301
Email: james.rickards (at) colorado.edu