- 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.