School of Mathematics Seminars and Lectures

Mobius Randomness and Horocycle Dynamics

by Prof. Peter Sarnak (Princeton University and Institute for Advanced Study, USA)

Wednesday, May 23, 2012 from to (Asia/Kolkata)
at Colaba Campus ( AG-66 )
Description
The Mobius function mu(n) is minus one to the number of distinct 
prime factors of n if n has no square factors and zero otherwise.
Understanding the randomness (often referred to as the `Mobius
randomness principle' in this function is a fundamental and very
difficult problem. We will explain a precise dynamical formulation of
the randomness and report on recent advances establishing it. In
particular the disjointness of the resulting Mobius Flow from 
horocycle flows and related horocycle dynamics at ``prime times''.