He will be particularly concerned with connecting primitive permutation groups to other questions in algebra, geometry and number theory including problems of polynomials over finite fields. . He will also study questions of how to generate finite simple groups and the eigenvalues of symmetric matrices over commutative rings. This is research in the subfield of algebra called group theory.
Group theory can be though of as the study of symmetry in the abstract.
As such, it has direct applications to areas of physics and chemistry. Much of group theory also connects directly to problems in coding theory and so has a direct bearing on the very practical problem of error correcting in data transfer. More on THIS Work .