- Undergraduate
- Graduate
- Research
- Algebraic and Arithmetic Geometry
- Applied Mathematics
- Computer Algebra
- Discrete Mathematics
- History of Mathematics
- Industrial Mathematics
- Mathematics, Genomics & Prediction in Infection & Evolution - MAGPIE
- Mathematics and Data
- Mathematics of Communications
- Number Theory
- Operations Research
- Centre for Operations Research and Decision Sciences
- PIMS at SFU
- Scientific Computing, Machine Learning and PDE

- People
- Math Internal Resources
- About Us
- Events | Outreach | News
- MATH EDI GROUP
- Grad Internal Resources
- Student Groups

# Nils Bruin

## Areas of interest

My research focusses on rational points on varieties. Of special interest are curves and Abelian varieties. For curves, p-adic analytic Chabauty methods in combination with algebraic covering techniques have recently yielded substantial results. The rational points of Abelian varieties, which form finitely generated groups called Mordell-Weil groups, form an important ingredient of those methods.

Mordell-Weil groups, and most importantly their free rank, are most commonly analysed using descent methods to compute Selmer groups. These provide a bound on the free rank but, unfortunately, not always a sharp one. The difference is measured by the Shafarevich-Tate group. Recently visualisation methods have been used to provide lower bounds on Shafarevich-Tate groups.

## Education

- Ph.D. Mathematics · Leiden University · 1999

**Research Areas**

### Courses

#### Fall 2024

#### Spring 2025

Future courses may be subject to change.