CRM: Centro De Giorgi
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From order to chaos - Pisa 2018

The difference between Lagrange and Markov after Hausdorff

speaker: Carlos Matheus Silva Santos ( CNRS)

abstract: After the remarkable works of Markov in 1879 and 1880, the Lagrange and Markov spectra (coding arithmetic properties of irrational numbers and indefinite binary quadratic forms) were studied by several authors (including Hurwitz, Perron, Hall, Freiman, Cusick, Flahive, . . . ). In this talk, we will discuss the complement of the Lagrange spectrum L in the Markov spectrum M. More precisely, after recalling the results of Freiman, Cusick and Flahive from the 70’s showing that MnL contains a countable, infinite subset, we will show that the Hausdorff dimension of M n L is strictly between 0 and 1.

Tue 10 Apr, 16:00 - 16:50, Aula Dini
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