26 May 2025 (Monday) 14:00 - 15:15  /  129-309

27 May 2025 (Tuesday) 14:00 - 15:15  /  129-309

28 May 2025 (Wednesday) 14:00 - 15:15  /  129-309

29 May 2025 (Thursday) 14:00 - 15:15  /  129-309

Title: Flat Geometry in Broader Contexts: A Journey Through Translation Surfaces

Abstract: In this mini-course, we will explore translation surfaces - flat geometric structures that have attracted significant attention from a dynamical perspective. Shifting the focus, these lectures will examine translation surfaces also through topological and geometric lenses, with the main goal of understanding the moduli spaces they inhabit, known as strata. We will begin with a general introduction to translation surfaces from both topological and complex-analytic viewpoints. I will then introduce the notion of periods and explain how translation surfaces can be represented through their period data. The final part of the course will focus on the so-called isoperiodic foliations, presenting recent developments in the field along with some open problems that remain at the frontier of current research.