| Speaker: | Kaveh Mousavand |
| Affiliation: | Okinawa Institute of Science and Technology |
| Location: | MC 5479 |
Abstract:Motivated by the representation theory of finite-dimensional algebras, we recently investigated the notions of left modularity and extremality in (completely) semidistributive lattices. For lattices of torsion classes, we obtain a simultaneous characterization of left modularity and extremality in terms of the behavior of certain indecomposable modules, called bricks. Our results extend the classical theory beyond the realm of finite lattices, while remaining within the framework of (completely) semidistributive lattices. Time permitting, I will also discuss extensions of these results to arbitrary infinite lattices that are completely semidistributive and weakly atomic. This talk is based on recent joint work with Sota Asai, Osamu Iyama, and Charles Paquette.
There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.