ProjektReelle Hurwitzzahlen
Grunddaten
Titel:
Reelle Hurwitzzahlen
Laufzeit:
01.03.2016 bis 31.10.2017
Abstract / Kurz- beschreibung:
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.
Schlüsselwörter:
Geometrie
geometry
Algebraische Geometrie
algebraic geometry
Beteiligte Mitarbeiter/innen
Leiter/innen
Rau, Johannes
Fachbereich Mathematik
Mathematisch-Naturwissenschaftliche Fakultät
Mathematisch-Naturwissenschaftliche Fakultät
Fachbereich Mathematik
Mathematisch-Naturwissenschaftliche Fakultät
Mathematisch-Naturwissenschaftliche Fakultät
Lokale Einrichtungen
Fachbereich Mathematik
Mathematisch-Naturwissenschaftliche Fakultät
Universität Tübingen
Universität Tübingen
Geldgeber
Bonn, Nordrhein-Westfalen, Deutschland
Bonn, Nordrhein-Westfalen, Deutschland