# ProjectReelle Hurwitzzahlen

## Basic data

Title:

Reelle Hurwitzzahlen

Duration:

3/1/2016 to 10/31/2017

Abstract / short description:

Hurwitz numbers count ramified covers of a Riemann sphere of a fixed degree and genus and with fixed ramification data. They provide interesting connections between various mathematical areas such as geometry, combinatorics and mathematical physics. In this proposal, we focus on real analogues of Hurwitz numbers. Tropical geometry can be viewed as a degeneration technique associating convex geometry objects to algebraic varieties that preserve many important properties. Tropical geometry has successfully been applied to problems in enumerative geometry, in particular to problems in Hurwitz theory and to real enumerative problems. In this project, we propose the systematic study of real Hurwitz numbers in the context of modern Hurwitz theory. The main tool will be tropical geometry.

On the one hand, we aim at new results in real enumerative geometry with the aid of tropical methods, on the other hand, we also envision progress in the area of tropical geometry, sharpening this tool for its use in Hurwitz theory.

On the one hand, we aim at new results in real enumerative geometry with the aid of tropical methods, on the other hand, we also envision progress in the area of tropical geometry, sharpening this tool for its use in Hurwitz theory.

Keywords:

geometry

Geometrie

algebraic geometry

Algebraische Geometrie

## Involved staff

### Managers

Rau, Johannes

Department of Mathematics

Faculty of Science

Faculty of Science

Department of Mathematics

Faculty of Science

Faculty of Science

## Local organizational units

Department of Mathematics

Faculty of Science

University of Tübingen

University of Tübingen

## Funders

Bonn, Nordrhein-Westfalen, Germany

Bonn, Nordrhein-Westfalen, Germany