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- Number theory
- asymptotic properties of families of global fields
- arithmetic statistics
- L-functions.
- -Arithmetic geometry
- algebraic curves over finite fields
- abelian varieties: point counting
- the invariant theory and classification of curves.
- Coding theory
- algebraic-geometric codes
- decoding algorithms.
- Cryptography
- elliptic curves and abelian varieties
- discrete logarithm problem
- pairings
- explicit computation of isogenies
- multiplication over finite fields
- APN functions
- bent and hyper-bent funtions