Cover Relations in the Lattice of Torsion Classes: Dynamics and Compatibility

In this talk we discuss combinatorial aspects of the lattice of torsion classes for a finite dimension algebra. It is well-known that the lattice of torsion classes is a semidistributive lattice. Finite semidistributive lattices can be characterized in a number of ways: by a special labeling of their cover relations; by a map which we call kappa from certain join-irreducible elements to meet-irreducible elements; and by a pairwise compatibility condition of join-irreducible elements and a dual compatibility condition of meet-irreducible elements. In this talk we will explore these three characterizations in the context torsion classes. This talk is based on joint work with Shijie Zhu, Gordana Todorov, and Eric J Hanson.