The Markov and Lagrange spectra and dynamical generalizations

Speaker:Carlos Gustavo Moreira
Time: Mon 16:30-17:30, 2019-10-21
Venue:Lecture Hall, Jin Chun Yuan West Bldg.


We will discuss some classical and recent results on the Markov and Lagrange spectra from Diophantine approximations. We will relate these results to symbolic dynamics, continued fractions and to the study of the fractal geometry of arithmetic sums of regular Cantor sets, a subject also related to the study of homoclinic bifurcations in Dynamical Systems. We will also present some recent results on dynamical generalizations of these spectra.


Carlos Gustavo Moreira was born in Rio de Janeiro in 1973 and concluded his Ph.D. at IMPA, under the supervision of Jacob Palis, in 1993. Moreira is a Full Professor of IMPA, where he is Professor since 1995. His main research areas are Dynamical Systems, Fractal Geometry, Number Theory (particularly Diophantine approximations) and Combinatorics. He is a Full Member of the Brazilian Academy of Sciences (since 2008) and of the TWAS (since 2012).
He was awarded a Gold medal at the IMO 1990, in Beijing, the UMALCA Prize in 2009, the TWAS Prize in Mathematics in 2010 and the Erdös Award of the WFNMC in 2018. He gave an invited talk at the Dynamical Systems session of the ICM 2014 in Seoul, a plenary talk at the ICM 2018, in Rio de Janeiro and a plenary talk at the 8th ICCM, in Beijing, in 2019.