Georgia Institute of Technology College of Sciences

 How can we recognize a map given certain combinatorial data? The Alexander method gives us the answer for self-homeomorphisms of finite-type surfaces. We can determine a homeomorphism of a surface (up to isotopy) based on how it acts on a finite number of curves. However, is there a way to apply this concept to recognize maps on other spaces? The answer is yes for a special class of maps, post-critically finite quadratic polynomials on the complex plane (Belk-Lanier-Margalit-Winarski). 

            In this talk, we will discuss Belk-Lanier-Margalit-Winarski’s methods, as well zome difficulties we face when trying to extend their methods to other settings.