  Over the past twenty years, lecture hall partitions have emerged as
fundamental combinatorial structures, leading to new generalizations and
interpretations of classical theorems and new results. In recent years,
geometric approaches to lecture hall partitions have used polyhedral geometry
to discover further properties of these rich combinatorial objects.
  In this paper we give an overview of some of the surprising connections that
have surfaced in the process of trying to understand the lecture hall
partitions.
