Title: Algebraic, geometric, and dynamical aspects of surfaces

Abstract: Taffy pullers, lab stirrers, and paint mixers are complicated dynamical systems.  To any such system we can ascribe a real number, called the entropy, which describes the amount of mixing being achieved.  Which real numbers arise, and what do they say about the dynamics of the system?  To address these questions, we view the above dynamical systems as homeomorphisms of surfaces.  In this talk, we will explore the theory of surface homeomorphisms, from the work of Max Dehn and Jakob Nielsen a century ago, to the revelations of the Fields medalist William Thurston in the 1970s, to the breakthroughs of Fields medalist Maryam Mirzakhani in the 21st century.