Pushing tilting theory to its limits

Classical tilting theory has been ubiquitous in the algebraist’s toolkit when it comes to understanding torsion theories — simply put, this is the question of classifying all factor- and extension-closed collections of modules over an algebra. Yet this easy-to-state classification problem has remained largely elusive and the answers produced by tilting theory remain incomplete in all but a handful of cases. I will describe a natural “completion of tilting theory” via convex-geometric constructions, namely the framework of “heart fans”, and explain how understanding the dynamics and limiting behaviour of tilting modules in this completed playground leads to classification results.

The talk is based on https://arxiv.org/abs/2502.05146.

Link: https://unipd.zoom.us/j/82518660070?pwd=RUpxL1FnZG9yVzFrOCtrM0xYMEZaZz09

Meeting ID: 825 1866 0070

Password: 62542