The main aim of this workshop is to expose participants to the interplay between geometry and combinatorics. The focus is on the combinatorial structures arising in geometric settings, in particular, hyperplane arrangements and lattice polytopes. The problems in these areas are rich with connections to other mathematical fields, including algebra, topology, number theory, and optimization. The topics that we plan to explore are: First, the combinatorics of hyperplane arrangements, in particular, we will see how to enumerate various-dimensional strata. We will learn all the standard techniques and discuss accessible open problems. Second topic is Ehrhart theory: a profound area that reveals intricate relationships between geometry, algebra, and combinatorics through the counting of integer points in polytopes. We will study Ehrhart polynomials, their reciprocity and also work on accessible open problems.

Note: The total number of lecture hours will be fewer (maybe six hours per speaker). The plan is to set  aside time to have students work on open problems in groups guided by the resource person and a tutor for part of the time.
Pre-requisites: First course in algebra, linear algebra and discrete mathematics.