Catalin Badea

Around Furstenberg’s “times 2, times 3” conjecture

For $n \geq 2$, let $T_n$ be the map $x \mapsto nx \bmod 1$ on the circle $\mathbb{T} = \mathbb{R}/\mathbb{Z}$. The aim of my talk is to present Furstenberg’s ``times 2, times 3'' conjecture: the only non-atomic probability measure on $\mathbb{T}$ that is invariant under both $T_2$ and $T_3$ is the normalised Lebesgue measure. I will also discuss some results obtained in connection with this conjecture, in collaboration with Sophie Grivaux. All necessary background will be reviewed in the talk.