The Southeast Geometry Seminar (SGS) is a semiannual series of one day event sponsored by:
We have a poster session. Please contact us if you would like to present a poster.
Abstract: The eigenvalues of the Laplace-Beltrami operator on a Riemannian manifold are an important set of geometric invariants of a compact manifold. For a complete, non-compact manifold the natural replacement for the eigenvalue spectrum is the set of resonances. We'll explain what resonances are in the context of hyperbolic surfaces, and discuss various recent results and conjectures on their distribution.
Abstract: I will describe the stability of liquid drops hanging in a gravity field and trapped between parallel planes. There are three modes of instability (instead of the two found by Wente in his analysis of rotationally symmetric pendant drops). Various aspects of the problem will be described including disconnected stable families and limits of zero gravity.
Abstract: We will discuss degenerations of Calabi-Yau metrics under algebraic geometric surgeries: extremal transitions or flops. We will prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related via extremal transitions and flops can be connected by a path consisting of continuous families of Ricci-flat Calabi-Yau manifolds and a compact metric space in the Gromov.CHausdorff topology. This is joint work with Yuguang Zhang of Tsinghua University.
Abstract: The volume product (Mahler volume) of origin symmetric convex body K is just a product of volume of K and its its dual/polar body. It turned out to be quite a useful object in Functional Analysis and Convex Geometry. Santalo inequality tell us that the volume product takes its maximal value at the Euclidean Ball. Mahler conjectured that the volume product is minimized by a cube. Despite many important partial results, the conjecture is still open in dimensions 3 and higher. In this talk we will discuss some recent progress and ideas concerning this conjecture.
Abstract: The classical inequality of Minkowski relates the total mean curvature of a convex surface to the area of the surface. I shall discuss a newly discovered Minkowski type inequality which can be interpreted as the Penrose inequality for collapsing shells in general relativity. This is joint work with Simon Brendle and Pei-Ken Hung.