Nils Bruin
Professor of Mathematics, Simon Fraser University
I work in number theory and arithmetic geometry. My motivating question is how to determine whether an equation has a solution in rational numbers and, if there are solutions, how to describe the set of solutions.
My students and I develop explicit methods for determining whether equations have solutions, for finding solutions if they exist, and for proving that a given list of solutions is complete. I also analyze how well such methods work.
In the process, we study abelian varieties, Jacobians of curves, Prym varieties, and moduli problems of curves with level structure. The methods we employ include finite descent, Brauer–Manin obstructions, Mordell–Weil sieving, and Chabauty methods, as well as rigorous numerical computation. We write software to support this research and contribute that software for use by others in various computer algebra systems.
Contact
- nbruin@sfu.ca
- Phone
- +1 778 782 3794
- Office
- SC K 10507
- PGP
- public key
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Department of Mathematics
Simon Fraser University
8888 University Drive
Burnaby, BC V5A 1S6, Canada
Seminar
Our Number Theory and Algebraic Geometry Seminar (NTAG) meets weekly on Thursdays during term.
Teaching
- Fall 2026MATH 151Calculus I
- Spring 2027MATH 440/740Galois Theory
- Spring 2027MATH 845Introduction to Elliptic Curves
Affiliations
- Department of Mathematics, Simon Fraser University
- Algebraic and Arithmetic Geometry group and Number Theory group at SFU
- CECM, Centre for Experimental and Computational Mathematics
- Associate Editor, Research in Number Theory