Dave Murphy, University of Verona 
Admissible Dissections of Surfaces and Piano Algebras

Admissible dissections of marked surfaces were used to classify gentle algebras and to provide a geometric model for their derived categories by Opper-Plamondon-Schroll. We introduce the notion of an extended admissible dissection of a marked surface, and the piano algebra associated to an extended admissible dissection.

We will discuss how the set of extended admissible diagrams of a marked disc without punctures is in bijection to the set of equivalence classes of a subset of classical generators of a Paquette-Yıldırım category. Further, we will see how the perfect derived category of a particular piano algebra is additively equivalent to a Paquette-Yıldırım category.


Georgios Dalezios, University of Verona   
On a class of quasi-hereditary algebras arising from Reedy categories

Abstract: The natural numbers and the weakly monotone functions between them form a category, called the cosimplicial indexing category, which is fundamental in the theory of simplicial sets. A Reedy category is a certain generalization, heavily used in homotopy theory. In this talk, we focus on Reedy categories having finitely many objects (any truncation of the cosimplicial indexing category is an example). We introduce a class of finite dimensional associative algebras, which we call Reedy algebras, and provide two main results. The first is that Reedy algebras are quasi-hereditary; the latter class of algebras was introduced by Cline, Parshall and Scott and has been studied extensively in representation theory. The second main result characterizes Reedy algebras as those quasi-hereditary algebras admitting a so-called Cartan decomposition. The talk is based on joint work with J. Stovicek and on joint work with T. Conde and S. Koenig.