A24: Lattice polytopes and representation theory


We will investigate the combinatorial and metric properties of various types of lattice polytopes. Our motivation stems from open questions in algebraic geometry and representation theory. For example, we investigate moduli spaces of toric degenerations of spherical varieties, induced by birational sequences and monomial bases of their coordinate rings. One goal we pursue is the description of Kostka numbers through lattice polytopes. Furthermore, we aim to make Newton-Okounkov bodies and their alternatives accessible through OSCAR.