Peigen Cao, Nagoya University

Title: Bongartz co-completions in cluster algebras and its applications

Abstract: A cluster algebra is a Z-subalgebra of a rational function field generated by a special set of generators called cluster variables, which are grouped into overlapping subsets of fixed size, called clusters. One can travel from one cluster to the others by a recursive process called mutation. In this talk I will introduce Bongartz co-completions in cluster algebras and give its applications to Fomin-Zelevinsky’s conjectures on denominator vectors and exchange graphs of cluster algebras.