报告题目：Ramified optimal transportation and its applications

报告人：夏青岚教授  美国加州大学戴维斯分校

报告时间：2016年3月14日（周一）下午16：00-17：00

报告地点：数学楼二楼学术报告厅

 
报告摘要: The optimal transportation problem aims at finding a cost
efficient transport from sources to targets. In mathematics, there are
at least two very important types of optimal transportation:
Monge-Kantorovich problem and ramified optimal transportation. In this
talk, I will give a brief introduction to the theory of ramified
optimal transportation.One motivation of the theory comes from the 
study of the branching structures found in nature. Many living systems
 such as trees, the veins on a leaf, as well as animal cardiovascular/
circulatory systems exhibit branching structures, as domany non-living
 systems such as river channel networks, railways,airline networks, 
electric power supply and communication networks.Why do nature and
 engineers both prefer these ramifying structures? What are the 
advantages of these branching structures over non-branching structures?
 These questions partially motivates us to explore the mathematics behind
 them. In this talk, I will talk about how to set up a mathematical theory 
for this general phenomenon in terms of optimal transport paths. An optimal
 transport path between  two probability measures can be viewed as a 
geodesic in the space of probability measures. In this talk, I will also
 survey some applications of the theory in multidisciplinary areas such as
 mathematical biology (e.g. the dynamical formation of tree leaves),metric 
geometry (e.g. the geodesic problems in quasimetric spaces),fractal geometry
 (e.g. the modified diffusion-limited aggregation),geometric analysis 
(e.g. transport dimension of measures) and mathematical economics (e.g. ramified
 optimal allocation problem).