Anna Barbieri - Università di Verona
Categories from marked surfaces and their exchange graphs

Abstract: A triangulation of a marked bordered Riemann surface induces a quiver (with potential) and a 3-Calabi-Yau triangulated category whose finite bounded t-structures and simple tilts between them are combinatorically related to “flipping” edges of the triangulation. Motivated by the study of stability manifolds, we generalize this picture: a mixed-angulation of a marked bordered Riemann surface defines a triangulated category obtained by Verdier localization of the former, and simple tilts of finite bounded t-structures still correspond to “flipping” edges of the mixed angulation. This talk is partly based on joint work with M.Moeller, Y.Qiu, and J.So.