Primitive tuning via quasiconformal surgery

Date: 
2020/01/17 Fri 14:00 - 17:00
Room: 
Room 609, Building No.6
Speaker: 
Weixiao Shen
Affiliation: 
Fudan University
Abstract: 

Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic polynomial can be tuned with an arbitrary generalized polynomial, generalizing a result of Douady-Hubbard for quadratic polynomials to the case of higher degree polynomials. This solves affirmatively a conjecture by Inou and Jiwi on surjectivity of the renormalization operator on higher degree polynomials in one complex variable. This is a joint work with Wang Yimin.