讲座标题
Fractal geometry of the Markov and Lagrange spectra and their set difference
讲座功夫
6月16日 16：00
讲座地址
学院路校区 2号楼309
主讲人
Carlos Gustavo Moreira
主办单元
数学科学学院
参加方式
本次院士大讲堂欢迎兄弟高校及全校师生校友参与参与，填写如下问卷即可报名参与
讲座撮要
We will discuss some recent results on the fractal geometry of the Markov and Lagrange spectra, M and L which are classical objects from the theory of Diophantine approximations, and their set difference. In particular, we discuss recent results in collaboration with Erazo, Gutiérrez-Romo and Roma?a, which give precise asymptotic estimates for the fractal dimensions of the Markov and Lagrange spectra near 3 (their smaller accumulation point) and other recent collaborations with Jeffreys, Matheus, Pollicott and Vytnova, in which we prove that the Hausdorff dimension of the complement of the Lagrange spectrum in the Markov spectrum has Hausdorff dimension between 0.594561 and 0.796445. Finally we will discuss a recent work in collaboration with H. Erazo, D. Lima, C. Matheus and S. Vieira in which we prove that inf(M\L)=3.
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 important for the study of homoclinic bifurcations in Dynamical Systems.
主讲人简介
Carlos Gustavo Moreira，现任巴西纯正与利用数学钻研所（IMPA）教授。Moreira教授是巴西科学院（BAC）院士，第三世界科学院（TWAS）院士，巴西数学奥猎欹克委员会（BMOC）成员。Moreira 教授重要钻研动力系统，在丢番图逼近，分形几何学等具体钻研领域做出了沉要贡献。他曾于1989年获得国际数学奥猎欹克（IMO)铜牌，1990年获得了国际数学奥猎欹克（IMO）金牌，2009年获得了UMALCA奖，2010年获得了TWAS奖，2018年获得国度数学较量世界联盟(WFNMC)宣告的保罗.厄多斯奖（Paul Erd?s Award）。他是2014年世界数学家大会（ICM）的45分钟汇报人以及2018年世界数学家大会（ICM）60分钟汇报人。
