Research-Fractal geometry and Diophantine approximations: the Markov and Lagrange spectra

Research

Dynamical Systems Seminar

Fractal geometry and Diophantine approximations: the Markov and Lagrange spectra

Speaker: Carlos Gustavo Tamm de Araújo Moreira ( Gugu ) , IMPA
Time: Nov 14, 2018, 16:10-17:30
Location: Conference Room 415, Hui Yuan 3#

Abstract: We will discuss recent results on the classical Markov and Lagrange spectra from Diophantine approximations, related to their (fractal) geometric structure. We will start discussing problems and results related to dynamical bifurcations and hyperbolic dynamics and its relations to regular Cantor sets, which have an important role in the study of the Markov and Lagrange spectra. We will also discuss recent results on natural generalizations in Dynamical Systems and Differential Geometry of these spectra.