Delucchi

Emanuele Delucchi 

Title: Group actions on posets and matroids with a view towards toric arrangements

Abstract: The study of symmetries of combinatorial structures is a classical subject that has appeared under many guises throughout history. One recent direction is in the context of extending matroid theory to the context of arrangement of subvarieties in the complex torus. In these lectures I will discuss some aspects of group actions on posets and simplicial complexes, with a special emphasis on the class of “translative actions” that seems to enjoy particularly nice structural properties in several contexts. I plan to focus on three main topics:
1) Group actions on (possibly infinite) posets and simplicial complexes and their Stanley-Reisner rings 
2) The combinatorial geometry of toric arrangements via equivariant matroid theory;
3) Some applications to equivariant Ehrhart Theory