Algebraic and Arithmetic Geometry

### Our research

Algebraic and arithmetic geometry are both concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarly with solutions lying in an algebraically closed field, while arithmetic geometry deals with the more subtle study of solutions lying in a number field or its rings of integers. Both these topics are central to mathematics, and have connections to subjects ranging from number theory and cryptography to mirror symmetry. Our individual research interests at SFU cover a broad spectrum, including toric geometry, linear subspaces of varieties, modular curves, and rational points on hyperelliptic curves.

## Faculty

Hyperelliptic curves, rational points, Chabauty methods, covering techniques, descent, local-to-global obstructions

Algebraic number theory, arithmetic geometry, representation theory, modular varieties, automorphic forms, diophantine problems, Galois representations, elliptic curves, Q-curves, function fields

Toric geometry, Fano varieties, mirror symmetry, deformation theory, linear subspaces of varieties, algebraic complexity theory

### Postdoctoral fellows and visitors

- Jens Bauch
- Mattia Talpo

### Graduate Students

- Avi Kulkarni
- Charles Turo