Fractal dimensions and Diophantine approximations
speaker: Carlos Gustavo Moreira (IMPA - INSTITUTO NACIONAL DE MATEMÁTICA PURA E APLICADA)abstract: We will discuss some problems of diophantine approximations related to fractal geome- try. We will discuss in particular some results on geometric properties and the fractal structure of the classical Markov and Lagrange spectra - in particular about the Hausdor dimensions of intersections of these spectra with half-lines: they always coincide and may assume (depending on the choice of the half-line) any real value in the interval 0; 1. We will also discuss a recent work in collaboration with Yann Bugeaud on (Lebesgue) typical real numbers from the point of view of diophantine approximations - we will see that, in a certain sense (related to Khintchine's theorem) there are no typical real num- bers from the point of view of diophantine approximations, and we will compute fractal dimensions of certain exceptional sets related to problems of this kind.
timetable:
Thu 13 Jun, 14:00 - 14:50, Aula Dini
documents:
Moreira Talk
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