Séminaires : Séminaire d'Algèbre

It is well known that the partially wrapped Fukaya category of a marked
disk is equivalent to the perfect derived category of a Dynkin quiver of
type A. In this talk I will present a higher-dimensional generalisation
of this equivalence which reveals a connection between three a
priori unrelated subjects:

* Floer theory of symmetric products of marked surfaces
* Higher Auslander-Reiten theory in the sense of Iyama
* Waldhausen K-theory of differential graded categories

If time permits, as a first application of the above relationship, I
will outline a symplecto-geometric proof of a recent result of Beckert
concerning the derived equivalence between higher Auslander algebras of
different dimensions. This is a report on joint work with Tobias
Dyckerhoff and Yankı Lekili.