kms 대한수학회

- April 15, 22 (Thursdays), 10 - 11 am Korea

- Professor Danny Calegari (University of Chicago)
- Title: Sausages and Butcher Paper (II)
- Abstract: 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.

- Zoom Link: April 15 https://us02web.zoom.us/j/81545856254
                    April 22 https://us02web.zoom.us/j/82708491826

- Poster:  http://newton.kias.re.kr/~choe/25th1.pdf