• Number Theory
  • Algebraic number theory
  • Class field theory
  • Algorithmic number theory
  • Asymptotic of number fields with given Galois group
  • Cohen-Lenstra heuristics of quadratic number fields
• Galois Theory
  • Computation of Galois groups
  • Inverse Galois theory
  • Explicit computation of polynomials with given Galois group
  • Embedding problems
• Computer Algebra
  • Software development in number and Galois theory
  • Creation of (mathematical) databases
  • Factorization of polynomials

Have a look at our database for field extensions of the rationals which contains polynomials for all Galois groups up to degree 19.