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Abstract

A few years ago, Morier-Genoud and Ovsienko introduced a q-deformation of the set of rational numbers. These q-deformed rational numbers, which we call "right q-rationals", enjoy fascinating combinatorial, topological, and algebraic properties. This talk will describe a different q-deformation, called the "left q-rationals", that we introduced in joint work with Louis Becker and Anthony Licata. The left q-rationals arose as natural partners to the right q-rationals while studying the action of the three-strand braid group on a category. I will discuss categorical interpretations of both of these q-rationals, and connections to Bridgeland stability conditions.