Alladi Ramakrishnan Hall

On Sarnak's conjecture

Sébastien Ferenczi

Institut de Mathématiques de Luminy

Sarnak's conjecture asserts that every sequence produced by a zero-entropy topological dynamical system is (asymptotically) orthogonal to the Mobius function.
I shall give a survey on recent results, including personal contributions, and focusing on two famous families of dynamical systems, interval exchanges and substitutions. I shall also give an idea of the various possible methods, with proofs of the simpler results.