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Dynamical Moduli Spaces

[HYBRID WORKSHOP] Connections Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables February 02, 2022 - February 04, 2022

February 02, 2022 (09:00 AM PST - 09:50 AM PST)
Speaker(s): Sarah Koch (University of Michigan)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Tags/Keywords
  • dynamical subvarieties

  • Moduli space

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

Dynamical Moduli Spaces

Abstract

A major goal in complex dynamics is to understand dynamical moduli spaces; that is, conjugacy classes of holomorphic dynamical systems. One of the great successes in this regard is the study of the moduli space of quadratic polynomials; it is isomorphic to the complex plane. This moduli space contains the famous Mandelbrot set, which has been extensively studied over the past 40 years. Understanding other dynamical moduli spaces to the same extent tends to be more challenging as they are often higher-dimensional. Many tools from complex analysis that pave the way for key breakthroughs in the one-dimensional setting do not carry over to higher dimensions. So instead of considering the whole moduli space, we follow an approach initiated by William Thurston and investigate special subvarieties of moduli space that give rise to dynamical moduli spaces. In this talk, we will explore the topology and geometry of the dynamical moduli spaces that play a prominent role in complex dynamics.

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92594?type=thumb Dynamical Moduli Spaces 16.1 MB application/pdf Download
Video/Audio Files

Dynamical Moduli Spaces

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