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Diophantine property in groups

Presented by: 
P Varjú University of Cambridge
Friday 4th July 2014 - 10:00 to 10:50
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons