**Nils Bruin**

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

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Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily 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 mathematicsâ€” and connect 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.

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

- Avinash Kulkarni

- Aven Bross
- Dan Lewis
- Charles Turo
- Sepehr Yadegarzadeh
- Sasha Zotine

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