Abstract: 

In 1980s, Douady-Hubbard developed a complex counterpart of the Feigenbaum renormalization theory for quadratic-like maps and used this theory to prove existence of small copies in the Mandelbrot set. Inou and Kiwi have extended most of Douady-Hubbard's theory to higher degree polynomial-like maps, but a key surjectivity property was left as a conjecture. We will show how to use quasiconformal surgery to prove this surjectivity conjecture by Inou-Kiwi, under a primitive assumption.  This is a joint work with Wang Yimin. 

Speaker: 

Prof. Shen made a series of breakthroughs in dynamical systems, including the solution of the real case of Fatou's conjecture. Fatou's conjecture was listed by the famous mathematician Smale as one of the most important mathematical problems of the 21st century. For these contributions, he won the CHERN Shiing S. Mathematics Award in 2009 and gave a 45-minute ICM lecture in 2014.