Theoretical Statistics and Mathematics Unit, ISI Delhi

April 17, 2017 (Monday) ,
3:30 PM at Webinar

Speaker:
Jean-Marc Deshouillers,
University of Bordeaux, France

Title:
Automatic sequences and Sarnak’s conjecture

Abstract of Talk

The distribution of prime number seems to have a high degree of randomness. Following Chowla, Sarnak introduced a conjecture according to which ‘primes are orthogonal to any sequence produced by a dynamical system of low complexity’. Sequences produced by a deterministic finite automaton have a low complexity and are good candidates for checking Sarnak’s conjecture. M\¨{u}llner proved that such sequences satisfy Sarnak’s conjecture. The special case when the automaton is synchronizing had been previously proved by him, Deshouillers and Drmota. In this talk in two independent parts, we shall present Sarnak’s conjecture and automatic sequences and outline the proof of M\¨{u}llner’s Theorem.
The first part, at JNU, will stress the Sarnak’s conjecture aspect.
The second part, at ISI Delhi, will stress the automatic sequences aspect.
Both parts will be self-contained.