Abstract: The (absolute logarithmic) Weil height is a nonnegative-valued function that can be thought of as measuring the arithmetic complexity of algebraic numbers. In particular, the points of height zero are precisely roots of unity, i.e. the torsion points in the multiplicative group of algebraic numbers. In 2000, Amoroso and Dvornicich proved a height gap for cyclotomic fields: for any algebraic number that is not a root of unity lying in some cyclotomic field, its height is greater than or equal to an absolute constant c>0. We will give an exposition of some key ideas in demonstrating that this height gap exists. We then look at the canonical height function associated to a rational map, which can be thought of as a dynamical analog to Weil height. We conclude with a statement of a conjecture analogous to Amoroso and Dvornicich's height gap in the setting of canonical height and dynamics.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: