Monday 4 September 2023, 15:00-16:00, Carslaw 535 Please join us in welcoming a new colleague on his first day at the university! Speaker: Justin Lanier (Sydney) Title: Recognizing topological polynomials by lifting trees Abstract: A polynomial can be viewed as giving a branched cover of a sphere over itself that is compatible with a complex structure. If handed a topological branched cover of the sphere, we can ask whether it can arise from a polynomialâand if so, which one? I’ll introduce these objects and share a combinatorial approach to this decision problem that draws from the theory of mapping class groups of surfaces; by iterating a lifting map on a complex of trees, we are able to certify whether or not a given branched cover arises as a polynomial. These results are joint work with Jim Belk, Dan Margalit, and Becca Winarski. I’ll also share some open problems and some paths of further investigation.