Seminario Geometría

Twisted surfaces and clusters of curves

Ponente:  Alastair King (University of Bath)
Fecha:  miércoles 07 de junio de 2023 - 11:30
Lugar:  Aula Naranja, ICMAT


I will describe how to associate to a triangulation of a surface with marked points a “twisted surface” together with a “cluster of curves” whose intersection matrix is the exchange matrix of cluster theory. The twisted surface is a combinatorial model for the spectral curve associated to quadratic differentials. The construction yields a groupoid representation that extends the Birman-Hilden representation of the braid group by Dehn twists. This is joint work with Qiu-Yu.