Georgia Institute of Technology College of Sciences

In the 20th century, Thurston proved two classification theorems, one for surface homeomorphisms and one for branched covers of surfaces.  While the theorems have long been understood to be analogous, we will present new work with Belk and Winarski showing that the two theorems are in fact special cases of one Ubertheorem.  We will also discuss joint work with Belk, Lanier, Strenner, Taylor, Winarski, and Yurttas on algorithmic aspects of Thurston’s theorem.  This talk is meant to be accessible to a wide audience.