turkmath.org

Tropical geometry and Berkovich spaces have been used to tackle many problems in classical algebraic geometry. The relation between them has important applications in both fields. In this talk I will give gentle introductions to both concepts. I will also give some details about higher dimensional tropical geometry and show a natural relation between tropicalizations of a variety and analytification of it in the sense of Berkovich. Then I will introduce linear tropicaliza- tions that gives a similar relation and has additional properties. I will talk about some applications of it to complex line arrangements and give a solution to transverse intersection problem in tropical geometry. This is a joint work with Özgür Ki ̧sisel.