course: Divisibility Sequences and Algebraic Groups

speaker: Joseph Silverman (Mathematics Department, Brown University)

abstract: A classical divisibility sequence is a sequence of integers D(n) with the property that if m divides n, then D(m) divides D(n). Famous divisibility sequences include aⁿ-bⁿ and the Fibonacci sequence. A very general construction associates a divisibility sequence to a rational point of infinite order in an algebraic group. In this talk I will describe this construction with many explicit examples, explain how Vojta's conjecture predicts growth bounds (some cases of which have been proven by Bugeaud, Corvaja, and Zannier), and discuss and give some numerical evidence for conjectural "lower bounds."

timetable:
Tue 21 Jun, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
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