Speaker: Daniel Stern (Cornell)

Title: New minimal surfaces via equivariant eigenvalue optimization (part I)

Abstract: I'll discuss recent work with Karpukhin, Kusner, and McGrath, in which we construct many new examples of embedded minimal surfaces in S^3 and free boundary minimal surfaces in B^3 with prescribed topology
via intrinsic shape optimization problems for Laplace and Steklov eigenvalues in the presence of symmetries. I'll describe some key analytic challenges in the existence theory for metrics
maximizing Laplace and Steklov eigenvalues on surfaces--with or without prescribed symmetry--and discuss new techniques for overcoming these, as well as some lingering open questions.
(To be continued in Peter McGrath's talk.)