Title:  Bases, polytopes and toric degenerations. 

Abstract: Finite dimensional irreducible modules of the Lie algebra sl(n) are of the key importance for the representation theory of simple Lie  algebras. 


We will construct monomial bases of the modules  compatible with the induced Poincaré–Birkhoff–Witt filtration. The bases are given in terms of certain convex polytopes.  We will explain the connection between the projective toric varieties associated to the above polytopes and the classical flag varieties. 


Based on joint works with Ghislain Fourier and Peter Littelmann.