# Twisted surfaces and clusters of curves

I will describe a combinatorial way to associate to a (tagged) triangulation of a surface with marked points and punctures a “twisted surface” together with a “cluster of curves” whose intersection matrix is the corresponding exchange matrix. The twisted surface roughly models the spectral curve associated to quadratic differentials, as in [Bridgeland-Smith], but the combinatorial construction has some subtle differences. This is joint work with Qiu-Yu.