The aim of this school is to explore and deepen the multifaceted connections
between algebra and combinatorics, highlighting how these fields influence and
enhance each other. The curriculum covers foundational topics such as graded
rings, Hilbert functions, free resolutions, and the relationship between symbolic
powers of ideals as well as the geometric properties of varieties, with a particular
focus on monomial ideals and their connections to graphs and simplicial
complexes. Key aspects of representation theory, including Young tableaux,