WEEKLY ACTIVITIES

Time: 9h, Thursday, May 28, 2020

Location: Room 507-508, Building A6, Institute of Mathematics

Abstract: In this talk, we show that for discrete time-varying linear control systems uniform complete controllability implies arbitrary assignability of dichotomy spectrum of closed-loop systems.

In Section I, we first define quivers and quiver mutation, and wish to present Fomin-Zelevinsky's definition of cluster algebras. We give an example of the clusters associated with quivers of type A_3 which is based on a combinatorial model for the mutation class of quivers of type A in terms of triangulation of a regular polygon. In the next section, we wish to provide two models for cluster algebras of type A. The first model is the homogeneous coordinate ring of the Grassmann variety, where the Plucker relations play the role of the exchange relations. The second model arises from the triangulation of a regular polygon which we studied in Section I. Here, the Ptolemy relations play the role of the exchange relations.