This project splits into two major portions. The first portion concerns the study of permutation representations. The principal investigator will classify all monodromy groups of primitive branched coverings of Riemann surfaces which are sufficiently large in terms of the genus. The second portion is concerned with how various properties of matrices and representations over a commutative ring are affected by extending the base ring. A group is an algebraic object having a multiplication defined on it. Groups occur naturally in many areas of mathematics, as well as chemistry and physics. This project is concerned with classifying monodromy groups.
