Speaker
Description
For a full exceptional sequence on the projective plane there is the famous Markov equation, which can be generalized to full exceptional sequences of length three in any triangulated category. There is also an application to cluster mutations in joint work with Beineke and Brüstle.
In this talk we define polynomial invariants for full exceptional sequences of length n. It turns out that such polynomial invariants define invariants of the triangulated category, so it is of interest to find them all. In this talk we determine generators for ring of polynomial invariants and study the connection to the natural braid group action. Moreover, we prove several properties and present examples. It turns out that polynomial invariants are closely related to the Coxeter transformation and the properties of the Grothendieck group together with its Euler form.
