Learning seminar in algebraic combinatorics: Torsion classes realize the Tamari lattice in type A

The protagonist of this talk will be the oriented quiver of Dynkin type A. We will introduce its (finitely many) indecomposable representations, use them to classify all quotient-closed subcategories of rep A_n, and discover which among these constitute torsion classes via "bracket vectors". The torsion classes ordered by inclusion recover the Tamari lattice, a beloved combinatorial lattice encoding a variety of known objects. This talk follows the paper "The Tamari lattice as it arises in quiver representations" by Hugh Thomas.