Yelin Ou, Texas A&M University-Commerce, will speak on:

The Geometry of Biharmonic Maps

Abstract:

Biharmonic maps are transformations between two spaces that minimize the bi-energy functional. Harmonic maps (e.g., geodesic, minimal surfaces, and holomorphic functions) form a special subclass of biharmonic maps so we call those non-harmonic biharmonic maps proper biharmonic maps. Examples of proper biharmonic maps are extremely difficult to find. In this talk, we will review some fundamental problems in the study of biharmonic maps, some known examples of proper biharmonic maps, and we will then present several methods that can be used to construct many new examples of proper biharmonic maps including biharmonic tori of any dimension in spheres, a family of biharmonic conformal immersions of cylinder into Euclidean 3-space, a foliation of proper biharmonic hypersurface in a conformally flat space, and some biharmonic maps between surfaces.

All students and faculty are welcome to attend!