Title: An introduction to quiver mutations and green sequences.

Abstract: Quiver mutation is an operation one can define on a directed graph that has shown to model the behavior of a large variety of mathematical objects including algebra, topology, physics and number theory. More specifically it arises when studying Teichmuller theory, total positivity of matrices, and even the behavior of high energy particle impacts. We will introduce the process of quiver mutation, and the proceed to explore quivers for a special sequence of mutations called maximal green sequences. The aim of the talk is to discuss recent work that allows one to build maximal green sequences for larger quivers by looking at "component preserving" sequences on induced subquivers. These new techniques have allowed us to construct maximal green sequences for large families of quivers where their existence was previously unknown.