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Seminar
FIELD Colloquium: Math
DATE April 22 (Thu), 2021
TIME 10:00-11:00
PLACE Online
SPEAKER Calegari, Danny
HOST Kim, Sang-hyun
INSTITUTE University of Chicago
TITLE Sausages and Butcher Paper II (KIAS Quadranscentennial Lectures)
ABSTRACT Zoom Link: https://us02web.zoom.us/j/82708491826
Poster : https://drive.google.com/file/d/1aUn9IV-SRJHajhMXDMUF8b4pg2qnK36k/view?usp=sharing

The shift locus S_d is the space of conjugacy classes of degree d polynomials f(z) in one complex variable for which all the critical points tend to infinity under repeated application of f. When d=2 this is the complement of the Mandelbrot set. Although S_d is a very complicated space geometrically, it turns out one can get a surprisingly concrete description of its topology; for example, S_2 is homeomorphic to an open annulus (this is equivalent to the famous theorem of Douady-Hubbard that the Mandelbrot set is connected). I would like to discuss two very explicit ways to capture the topology of S_d, one via the combinatorics of laminations (Butcher paper) and one via algebraic geometry (sausages). As a corollary of this explicit description one can show that S_d is a K(pi,1) with the homotopy type of a complex of half its real dimension.
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