Overview of the lattice of torsion classes

A torsion class is a collection of modules for an algebra that is closed under quotients and extensions. It turns out that many combinatorial objects can be realized as torsion classes for certain algebras, and the containment order on torsion classes recovers interesting partial orders on those objects. We will give a brief introduction to several examples, including the Tamari lattice, the weak order, and the oriented exchange graph of a cluster algebra. We will also outline the schedule for the first half of the semester.

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Date published: Wednesday, January 21, 2026