Geometry & Topology: Justin Lanier -- Recognizing topological polynomials by lifting trees

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 polynomial—and 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.