### Diophantine property in groups

Varjú, P *(University of Cambridge)*

Friday 04 July 2014, 10:00-10:50

Seminar Room 1, Newton Institute

#### Abstract

Let x, y be two real numbers and consider all numbers that can be expressed from them using addition and subtraction. Denote by B_l the set of numbers that can be obtained by using x and y at most l times. A simple Borel-Cantelliargument shows that the smallest positive element of B_l is at least cl^(-1-e) for almost all pairs x,y. In the lecture we will investigate the analogue of this property in non-commutative Lie groups.

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