Dyck Paths, Configuration Spaces and Polytopes for Linear Nakayama AlgebrasOberseminar Algebra und Darstellungstheorie

by Veronica Calvo Cortes (MPI MiS Leipzig)

Thursday Apr 30, 2026, 4:15 PM → 5:15 PM Europe/Berlin

Endenicher Allee 60/1-008-Seminarraum (Mathezentrum)

We present a combinatorial model of configuration spaces and polytopes associated to linear Nakayama algebras. Such configuration spaces were recently introduced for more general algebras by Arkani-Hamed, Frost, Plamondon, Salvatori and Thomas. In our special setting, we provide elementary proofs and explicit combinatorial constructions. From a Dyck path we define three related objects: a finite-dimensional algebra, an affine algebraic variety, and a polytope. Moreover, our constructions are natural: each relation in the poset of Dyck paths gives a morphism between the corresponding objects.