Toric degenerations: a bridge between representation theory, tropical geometry and cluster algebras

In this talk I will explain the basic idea of toric degenerations and give an overview on where and how these arise. The motivation is to deform arbitrary (projective) varieties to toric varieties. This is desirable as toric varieties are particularly nice, many of their algebraic and geometric properties are encoded in combinatorial or polyhedral data.

I will explain three approaches (mentioned in the title) to constructing toric degenerations using valuations and show how they are related. The main example will be toric degenerations of Grassmannians, in particular Gr(2,n).