Mathematics Colloquium
Date: Wednesday, 6 August 2025
Time: 3.30 PM
Venue: Seminar Hall
Marked cycle curves for quadratic polynomials and rational maps
Malavika Mukundan
Boston University.
06-08-25

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Abstract

Given any analytic function with a marked periodic cycle, we may perturb this function in some natural parameter space of functions and track the changes in the marked cycle. This gives rise to a marked cycle curve, which is a branched covering space over the parameter space. In this talk, we discuss marked cycle curves over two spaces of functions: quadratic polynomials, and quadratic rational maps with a critical 2-cycle. We will see how these curves are related to one of the fundamental objects in complex dynamics - the Mandelbrot set. This is joint work with Caroline Davis, Giulio Tiozzo and Daniel Stoll. Please note that this talk will be accessible to undergraduates.