Geometry & Topology Seminar: Reflections on Bubbles and Films

Abstract: Since the work of Alexandrov in the 1950s, the presence of reflection symmetries has been a key to understanding the geometry of constant mean curvature and minimal surfaces embedded in 3-dimensional space forms.  Three decades later, this opened the door to a moduli space theory for such surfaces, particularly sub-moduli spaces of coplanar surfaces, with surprising connections to Teichmüller theory and CP^1-structures.  We'll discuss our long-standing work on these moduli spaces, along with recent work (with McGrath, and later with him, Karpukhin and Stern) employing an intrinsic reflection to classify free boundary minimal annuli and construct free boundary minimal surfaces of every topology embedded in B^3, as well as many more closed embedded minimal surfaces of low area in S^3, and (most recently) nonorientable embedded minimal surfaces of low area in S^4 of every topological type.

Host: Charles Ouyang