Boulos El Hilany

Title: Signed counts of real simple rational functions 

Abstract: 
In this talk, I will describe the problem of counting real simple rational functions f with 
prescribed ramification data (i.e. a particular class of oriented real Hurwitz numbers of 
genus 0). I will introduce our signed count of such functions that is invariant under change 
of the branch locus, thus providing a lower bound for the actual count (which does depend 
on such change). I will outline (non-)vanishing theorems for these signed counts and study 
their asymptotic growth when adding further simple branch points. The approach is based 
on the works of Itenberg and Zvonkine which treats the polynomial case. 
This is a joint work with Johannes Rau.