Towards a computational theory of heights

10/15/2013 - 12:15pm
10/15/2013 - 1:10pm
David Krumm (CMC)

The theory of height functions on algebraic varieties has long been an essential tool in Diophantine geometry. Indeed, the proofs of several of the fundamental results in this area (such as the Mordell-Weil theorem, Siegel's theorem, and Faltings' theorem) rely heavily on the properties of height functions. It is therefore to be expected that heights will play an important role in the developing field of computational Diophantine geometry, which seeks to enable the explicit computation of rational points on varieties over number fields. This talk will be focused on the problem of computing all points of bounded height in projective spaces over number fields, and possible applications of an algorithm that would solve this problem.

Mudd Science Library 126, Pomona College