107/2/27黃彥彰 教授 (信陽師範學院)
主講人: 黃彥彰 教授 (信陽師範學院)
題 目：A problem of existence of horizontal envelops in the 3D-Heisenberg group and its application
One of interesting problems in classical geometry is to find the envelope for a family of lines or hypersurfaces in the Euclidean spaces and several applications to Economics and Mathematical Optimization have been developed. In this talk, regard the 3D-Heisenberg group as the standard model of sub-Riemannian manifolds, we will show the necessary and sufficient conditions for the existence of horizontal envelops in the 3D-Heisenberg group by using the standard techniques in Integral Geometry. Connecting to Data Science, an application to optimizing the objective function defined on a given dataset will also be introduced. We obtain a method to construct horizontal envelopes from the given ones and characterize the solutions satisfying the construction. The similar results can be generalized to the higher dimensional Heisenberg groups.
日 期：107年2月27日(星期二) 16:10~17:00
茶 會： 15:30~16:00數學館四樓409室舉行