Mounir Nisse, Université de Paris 6, France

Complex and Non-Archimedean Coamoebas

 

Abstract

Amoebas (resp. Coamoebas) are the link between the classical complex geometry and the tropical (resp. complex tropical) geometry. I will start by briefly introducing these objects in the complex algebraic hypersurfaces cases.

 

The purpose of my talk will be to explain the relation between complex and non-Archimedean coamoebas on one hand, and Newton polytope on the other hand. Moreover, a brief survey of the further development of complex and non-Archimedean amoebas will be given, as well as a description of some new results.

 

However, the same circle of ideas used on amoebas, also shows that the coamoebas have a similar geometric and combinatorial structure. Application for n = 2 will be outlined. Many examples, with pictures, will be given.