Learning Seminar in Algebraic Combinatorics @ University of Michigan
Topic: The Lattice of Torsion ClassesMeetings: Wednesdays 2:30pm--3:30pm in East Hall 4088
Organizers: Grant Barkley, Thomas Lam, Yelena Mandelshtam, George H. Seelinger.
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Winter 2026 Talks
01/21/26 »
Grant Barkley:
Overview of the lattice of torsion classes
Abstract
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.