Abstract
The aim of this minicourse will be to explain how cluster combinatorics arises naturally in the study of 3-Calabi-Yau triangulated categories. I will begin by introducing some basic material from homological algebra: triangulated categories and t-structures. These topics will be covered in more-or-less detail depending on the background of the audience. Then I will introduce the basic operation of tilting and explain how in the case of 3-Calabi-Yau categories it leads to the quiver mutation rule. I will also introduce the space of stability conditions and show how the exchange graph arises as the dual graph to a natural cell decomposition. If there is enough time I'd also like to discuss how the cluster mutation rule comes about from the wall-crossing formula in Donaldson-Thomas theory. There are some excellent lecture notes on closely related topics by Bernhard Keller (https://arxiv.org/pdf/1102.4148),