# Seminars & Colloquia Calendar

Colloquia

## Irreducibility in complex dynamics: some open problems and new results

#### Sarah Koch (U. of Michigan)

Location:  Hill 705
Date & time: Wednesday, 27 February 2019 at 3:30PM - 4:30PM

Abstract: Complex dynamics is centered around studying rational functions on the Riemann sphere from the point of view of iteration. In this talk, we begin with the family of quadratic polynomials, a great success story that involves the famous Mandelbrot set. The family of quadratic polynomials naturally lives inside the moduli space of quadratic rational maps, which is isomorphic to $$C^2$$. We will introduce the Milnor curves inside this moduli space; these are dynamically-defined algebraic curves. A major open problem in the subject is to determine if these curves are connected. We present the first result establishing that an infinite collection of them are irreducible over complex numbers. Our proof uses arithmetic techniques.

This is joint work with Xavier Buff and Adam Epstein.

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