Speaker: Oishee Banerjee
Date: November 28, 2019
Affiliation: Hausdorff Center of Mathematics (Bonn)

Abstract: In this talk we will discuss the moduli spaces Simp$^m_n$ of degree $n+1$ morphisms $\mathbb{A}^1_{K} \to \mathbb{A}^1_{K}$ with ``ramification length $ < m$'' over an algebraically closed field $K$. For each $m$, the moduli space Simp$^m_n$ is a Zariski open subset of the space of degree $n+1$ polynomials over $K$ up to Aut$(\mathbb{A}^1_{K})$. It is, in a way, orthogonal to the many papers about polynomials with prescribed zeroes- here we are prescribing, instead, the ramification data. We will see why and how our results align, in spirit, with the long standing problem of understanding the topology of the Hurwitz space.