Title: Properties of s-lecture hall polytopes

Abstract: Arising from the well-studied s-lecture hall partitions, we will discuss the s-lecture hall polytopes. In recent work, T. Hibi, A. Tsuchiya, and I were able to characterize algebraic and geometric properties for  s-lecture lecture hall polytopes, such as the Fano, reflexive, and Gorenstein properties as well as the integer decomposition property (IDP), for certain classes of s-sequences. We also make several conjectures. At the end of the talk, we will briefly discuss related polytopes, namely the partition polytope and the Gelfand–Tsetlin polytope, and recent work of P. Alexandersson which suggests that our conjectures may not be true.