Final Activity Report Summary - MODULAR APPROACHES (Modular and classical approaches to diophantine equations)
Fermat Last Theorem was, for over 350 years, the most famous problem in Mathematics. It was finally resolved in 1995 by Andrew Wiles. Fermat's Last Theorem is an instance of a Diophantine equation. This is an equation where we want all solutions that are integers (whole numbers). Wiles pioneered what is called "the modular approach to Diophantine equations". The older (pre-Wiles) approaches are called "the classical approaches to Diophantine equations". It is natural to ask for the relationship between the modular and classical approaches and whether they can go hand-in-hand to help solve other famous problems.
The project has been highly successful in furthering our understanding of the modular approach and how it interacts with older approaches to Diophantine equations. Important progress has been made on several outstanding Diophantine problems. For example, in joint work with Imin Chen (Simon Fraser University, Canada), the fellow shows solves the famous Kraus equation for 62% of all possible exponents.
The project has been highly successful in furthering our understanding of the modular approach and how it interacts with older approaches to Diophantine equations. Important progress has been made on several outstanding Diophantine problems. For example, in joint work with Imin Chen (Simon Fraser University, Canada), the fellow shows solves the famous Kraus equation for 62% of all possible exponents.