| Colloquia Novel Perspectives in Understanding the Geometry of Surfaces and Manifolds Hung Tran Department of Mathematics and Statistics, Texas Tech University |
The second theme is the search for a hierarchy of stationary surfaces, which are critical points of a certain geometric functional. In Calculus, we use derivative tests to classify critical points and determine whether one is a minimum, a maximum, or a saddle. An abstract generalization is to study the index of an operator associated with the second variation. In this direction, we develop a novel mechanism, via partial differential equations when studying surfaces with boundaries, with several applications. Specifically, there is a partial resolution of a conjecture proposed by R. Schoen and A. Fraser and closely related to the Willmore conjecture. Another significant contribution is to introduce a new approach based on functional analysis to investigate a setup with constraints.
Dr. Hung Tran's Tenure and Promotion Colloquium has been archived in the Mediasite catalog.