Abstract

We will discuss new categorical interpretations of two distinct g-deformations of the rationalnumbers. The first one, introduced by Morier-Genoud and Ovsienko in a diferent context, enjoysfascinating combinatorial, topological, and algebraic properties. The second one is a natural partnelto the first, and is new. We obtain these deformations via boundary points of a compactification ofthe space of Bridgeland stability conditions on the 2-Calabi--.Yau category of the A2 quiver. The talkis based on joint work with Louis Becker, Anand Deopurkar, and Anthony Licata.