About me
I am an Assistant Professor at Saint Mary's University, in Halifax, Nova Scotia, Canada.
Between 2021 and 2024, I was 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.
Due to frequent moving while growing up, I do not have a canonical hometown. That said, I normally identify with being from Annapolis Royal, Nova Scotia.
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;
- (indefinite) quadratic forms and (indefinite) quaternion algebras;
- arithmetic Fuchsian/Kleinian groups, especially their fundamental domains and geodesics.
Updates
- 4 September 2024: Start of the new academic year!
- 15 - 19 July 2024: Attended ANTS XVI at MIT.
- 17 June 2024: The Local-Global Conjecture for Apollonian circle packings is false is accepted to the Annals of Mathematics!
- 3 - 14 June 2024: Attending Computational Aspects of Thin Groups at National University of Singapore.
- 15 May 2024: Talk at UC Davis.
- 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.
Contact
Department of Mathematics and Computing Science
Saint Mary's University
923 Robie Street
Halifax, NS B3H 3C3
Canada
Office: McNally North 120
Email: james.rickards (at) smu.ca