Parameter spaces in complex dynamics and related topics

Global Combinatorics for Per_n(0) Curves

speaker: Caroline Davis (Indiana University)

abstract: The moduli space of quadratic rational maps with a critically marked $n$-cycle is an algebraic curve called Per_n(0). A longstanding open conjecture in rational dynamics asks whether this curve is irreducible, which is equivalent to Per_n(0) being smooth and connected. Epstein showed Per_n(0) is smooth, so to resolve the conjecture it suffices to show that Per_n(0) is connected. In this talk we use the dynamics of quadratic polynomials' Hubbard trees to answer when two polynomials in Per_n(0) are close in the sense of having shared matings or captures. One upshot is we show Per_n(0) is connected in a certain combinatorial category.

timetable:
Tue 28 May, 16:45 - 17:25, Aula Dini
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