Serious Gaming oder: Spielen ernst nehmen

Vortragende Person/Vortragende Personen:
Boulos El-Hilany

Two continuous maps $f, g : \mathbb{C}^2\longrightarrow\mathbb{C}^2$ are said to be topologically equivalent if there are homeomorphisms $\varphi,\psi:\mathbb{C}^2\longrightarrow\mathbb{C}^2$ satisfying $\psi\circ f\circ\varphi = g$.
It is known that there are at most finitely many topologically non-equivalent polynomial maps above with any given degree $d$.
The number of these topological types is known only whenever $d=2$.

Recently, we provided a description of several topological invariants for generic complex polynomial maps on the plane sharing a pair of Newton polytopes of a certain type. In this talk, I will present this description, together with the consequent tool for constructing topologically non-equivalent maps of degree $d$. In turn, we obtain non-trivial lower bounds on their numbers.
This is a joint work with Kemal Rose.