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

IMPA, Brasil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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

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