Abstract: We will talk about recent work showing there are infinitely many primes with no 7 in their decimal expansion. (And similarly with 7 replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most X1−c elements less than X) which is typically vey difficult.
The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, combinatorial geometry as well as tools from analytic number theory.

Recording during the thematic meeting : "Ergodic Theory and its Connections with Arithmetic and Combinatorics" the December 13, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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