講座題目
Fractal geometry of the Markov and Lagrange spectra and their set difference
講座時間
6月16日 16：00
講座地點
學(xué)院路校區(qū) 2號樓309
主講人
Carlos Gustavo Moreira
主辦單位
數(shù)學(xué)科學(xué)學(xué)院
參與方式
本次院士大講堂歡迎兄弟高校及全校師生校友到場參加，填寫如下問卷即可報名參加
講座提要
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.
主講人簡介
Carlos Gustavo Moreira，現(xiàn)任巴西純粹與應(yīng)用數(shù)學(xué)研究所（IMPA）教授。Moreira教授是巴西科學(xué)院（BAC）院士，第三世界科學(xué)院（TWAS）院士，巴西數(shù)學(xué)奧林匹克委員會（BMOC）成員。Moreira 教授主要研究動力系統(tǒng)，在丟番圖逼近，分形幾何學(xué)等具體研究領(lǐng)域做出了重要貢獻(xiàn)。他曾于1989年獲得國際數(shù)學(xué)奧林匹克（IMO)銅牌，1990年獲得了國際數(shù)學(xué)奧林匹克（IMO）金牌，2009年獲得了UMALCA獎，2010年獲得了TWAS獎，2018年獲得國家數(shù)學(xué)競賽世界聯(lián)盟(WFNMC)頒發(fā)的保羅.厄多斯獎（Paul Erd?s Award）。他是2014年世界數(shù)學(xué)家大會（ICM）的45分鐘報告人以及2018年世界數(shù)學(xué)家大會（ICM）60分鐘報告人。
