David Masser has made important contributions to transcendence and diophantine geometry. His early work on zero estimates on group varieties was a crucial step in the ultimately successful goal, finally achieved by Gisbert Wüstholz, of establishing the natural generalisation to algebraic groups of the theory of logarithmic forms. As a consequence of this development, there is now considerable and fruitful interplay between transcendence theory and many aspects of arithmetical algebraic geometry. As an example, David and Gisbert obtained in this way a new proof of a fundamental conjecture of Tate and thus made effective a central component of Gerd Faltings’ famous work on the Mordell conjecture. In an entirely different context, David is also responsible, following an earlier insight of Joseph Oesterlé, for formulating the abc conjecture; this is a simple statement about integers which seems to hold the key to much of the future direction of number theory.
Subject groups
- Mathematics
Pure mathematics
