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Description

In this talk, I will give an introduction to the theory of ramified optimal transportation as well as its applications to both pure and applied mathematics. In terms of applied mathematics, transport paths are used to model many "tree shaped" branching structures, which are commonly found in many living and nonliving systems. Trees, lungs, river channel networks, are just some examples. On the other hand, optimal transport paths provide excellent examples for studying geodesic problems in quasimetric spaces, where the distance functions do not necessarily satisfy the usual triangle inequality, but satisfy a relaxed triangle inequality.