Complex Analysis and Dynamics Seminar
Fridays 2:00 - 3:00 pm
Room 5417
Organizers: David Aulicino, Ara Basmajian, Patrick Hooper, Jun Hu
Past seminars:
- Fall 2006
- Spring 2007
- Fall 2007
- Spring 2008
- Fall 2008
- Spring 2009
- Fall 2009
- Spring 2010
- Fall 2010
- Spring 2011
- Fall 2011
- Spring 2012
- Fall 2012
- Spring 2013
- Fall 2013
- Spring 2014
- Fall 2014
- Spring 2015
- Fall 2015
- Spring 2016
- Fall 2016
- Spring 2017
- Fall 2017
- Spring 2018
- Fall 2018
- Spring 2019
- Fall 2019
- Spring 2020
- Fall 2021
- Spring 2022
- Fall 2022
For information about the history of our seminar, please visit: History.
Spring 2023:
February 10: Alex Kapiamba (University of Michigan)
Elephants all the way down: the near-parabolic geometry of the Mandelbrot set
Understanding the geometry of the Mandelbrot set, which records dynamical information about every quadratic polynomial, has been a central task in holomorphic dynamics over the past forty years. Near parabolic parameters, the structure of the Mandelbrot set is asymptotically self-similar and resembles a parade of elephants. Near parabolic parameters on these "elephants'', the Mandelbrot set is again self-similar and resembles another parade of elephants. This phenomenon repeats infinitely, and we see different parades of elephants at each scale. In this talk, we will explore the implications of controlling the geometry of these elephants. In particular, we will partially answer Milnor's conjecture on the optimality of the Yoccoz inequality, and see potential connections to the local connectivity of the Mandelbrot set.
March 24: Saeed Zakeri (Queens College and The Graduate Center)
TBA
March 31: Andrey Gogolev (The Ohio State University)
TBA