Flat surfaces and their Teichmüller theory have played a central role through their connections to many other areas of mathematics, such as dynamical systems (via polygonal billiards), algebraic geometry (via divisors and bundles), and low-dimensional topology (via mapping class groups).

The study of dynamics on Teichmüller space was revolutionized by the “magic wand” theorem of Eskin and Mirzakhani, which precipitated countless breakthroughs in fields ranging from dynamics to algebraic geometry and low-dimensional topology. Recently, several major results have appeared which push the “magic wand” theorem to new arenas. A broad goal of this conference is to assemble researchers who are working on applying the “magic wand” theorem and pushing it to new settings.

A parallel track at the conference is to apply recent breakthroughs to study the geometry of Teichmüller space and related moduli spaces of geometric structures. In short, this conference will push the “magic wand theorem” to new settings and bring together communities whose work is essential to pioneering its exciting new applications.

CMI Enhancement and Partnership Program