Title：An algebraic proof of Thurston transversality for bicritical polynomials
Speaker：彭俊文博士（理論中心）
Time：2021.12.20 (Mon.) 16:00 – 17:00
Venue：第三綜合大樓2F 201
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Tea time：15:30, Room 707
Abstract:
Thurston transversality is a celebrated result of holomorphic dynamics. Roughly speaking, Thurston showed that curves given by dynamical conditions intersect transversally. Let me give an easy example to illuminate the idea. The critical point of the polynomial $f_c(x)=x^2+c$ is 0. And, we may wonder how many solutions $c\in\mathbb{C}$ we have if 0 has a period, say 3. This question is precisely equivalent to solving the equation $f^3_c(0)=0$ where $f^3_c$ is the third iterate of $f_c$. Thurston transversality then says there must be 4 distinct solutions because $f^3(0)$ is a degree 4 polynomial in terms of $c$. In this talk, we will give an algebraic proof of Thurston transversality in the periodic case for bicritical polynomials. This is also the first algebraic proof for bad reduction.
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