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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