9400833 Larsen This award funds the investigations of Prof. Michael Larsen into monodromy representations of fundamental groups especially as they arise in number theory. Prof. Larsen will attempt to compute monodromy groups in particular cases and study variations caused by changes in the base data. He would like to be able to construct examples where the monodromy group is prescribed beforehand, an inverse problem based on the invariants of the induced representation. This is research in the field of arithmetic algebraic geometry, a subject that combines the techniques of algebraic geometry and number theory. In its original formulation, algebraic geometry treated figures that could be defined in the plane by the simplest equations, namely polynomials. Number theory started with the whole numbers and such questions as divisibility of one whole number by another. These two subjects, seemingly so far apart, have in fact influenced each other from the earliest times, but in the past quarter century the mutual influence has increased greatly. The result has been an increased understanding of both areas of mathematics.
