On Thue's Equation and the ABC-Inequality (Number Theory): VPW award

In projects (1) and (2) the focus is on obtaining bounds on the number of integral solutions of certain classes of diophantine equations over function fields which depend only on the number of monomials of the equation. This problem which seemed so inaccessible a few years ago, has recently made significant progress and the success is largely due to the abc- inequality. The proposed research in project (3) is to investigate Siegels conjecture over complex number fields. Project (4) deals with Thue's equation F(x,y)=1 over the rational. The object here is to show that the number of integral solutions can be bounded in terms of the number of large coefficients of F only. The project is in an area of number theory where the methods of proof are extremely complicated and technical. It furthers VPW program objectives to provide opportunities for women to advance their careers in science or engineering through research, and to encourage other women to pursue careers in these areas through the investigators' enhanced visibility as role models on the host campuses. In this project, the proposed activities which contribute to the second objective include: teaching a graduate course, co-sponsoring the Number Theory seminar, and organizing a new seminar. The aim of the last project is to offer women mathematicians greater stimulation in research and interaction with other mathematicians.