## View abstract

### Session S09 - Number Theory in the Americas

Thursday, July 22, 18:30 ~ 19:00 UTC-3

## Fractal geometry of the Markov and Lagrange spectra and their set difference

### Carlos Gustavo Moreira

We will discuss some recent results on the fractal geometry of the Markov and Lagrange spectra from Diophantine approximations, and their set difference - in particular we show, in collaboration with Carlos Matheus, Mark Pollicott and Polina Vytnova that the smallest element $t_1$ of the Lagrange spectrum $L$ such that $L\cap (-\infty,t_1)$ has Hausdorff dimension $1$ has decimal representation starting by $0.334384$, proving rigorously and improving previous heuristic estimates by R. Bumby, which suggest that \$0.33437