Description:

Title: Density of Twist of Tori on Moduli Spaces

Abstract: A translation surface is horizontally periodic if every horizontal trajectory is either closed or connects singularities. Such surfaces can be built by gluing horizontal cylinders together along their boundaries. Applying the horocycle flow independently to each cylinder produces a natural torus-worth of surfaces in moduli space, which we think of as a “higher-dimensional periodic horocycle.” We will discuss criteria ensuring that these tori become dense when pushed forward by the Teichmüller geodesic flow, as well as the rigidity questions for horocycle flows that motivate this problem.  No prior familiarity with these objects will be assumed.  Joint work with Jon Chaika.