报告题目1：Poset Representation Theory and Some of Its Practical Applications
报告内容简介：In this talk, we describe mainly the theory of representation of equipped posets, the matrix problems associated to this theory and some applications in different fields of computer science. In particular, it is discussed the use of the algorithms of differentiation for equipped posets in order to model warfare strategies and interactions between computer worms and viruses..
报告题目2：A geometric realization of socle-projective categories for posets of type A
报告内容简介：In this talk, we show a link between the theory of cluster algebras and the theory of representations of posets. Particularly, we give a geometric interpretation of the category of finitely generated socle-projective representations over the incidence algebra of a poset of type A as a combinatorial category of certain diagonals of a regular polygon. This construction is inspired by the realization of the cluster category of type A as the category of all diagonals by Caldero-Chapoton-Schiffler. Moreover, given a poset P of type A, we define a subalgebra A(P) of a cluster algebra A and we establish a sufficient condition to conclude that A = A(P). This is a joint work with R. Schiffler.
报告题目3：Equipped Posets and Its Auslander-Reiten quiver
报告内容简介：The theory of representation of equipped posets is a generalization of the theory of representation of ordinary posets developed by Nazarova, Roiter and their students in the 1970’s. The main goal of such theories is to give a complete description of the indecomposable objects and irreducible morphisms of a category of representations rep P of a given poset P. In this talk, we present a little review of this kind of posets, its indecomposable objects, its irreducible morphisms, its category of representations, and a combinatorial algorithm to build its Auslander-Reiten quiver.