Date & Time: Tuesday, July 23, 2013, 4 p.m.

Venue: Ramanujan Hall

Title:Spectral properties of the Möbius function and a random Möbius model

Speaker: Prof. El Houcein El Abdalaoui,Labo. de Maths Raphael SALEM, Avenue de l'Université, BP.12, 76801 Saint Etienne du Rouvray - France

Abstract: In this talk, we will review some recent results on the Sarnak conjecture on the orthogonality of Möbius function to the dynamical systems with zero topological entropy. Furthermore, we recall some basic fact on Möbius function and finally, using a spectral analysis of Möbius function, we proved that Sarnak conjecture is related to Elliott conjecture in the Number Theory. In the case of random model, we are able to prove that Sarnak conjecture holds a.e.

This is my recent work with my colleague M. Disertori.