Speaker
Description
In this seminar I will review the theory of flat G-chains, as they were introduced by H. W. Fleming in 1966, and currents with coefficients in groups with the aim of showing some recent applications to variants of the branched optimal transport. One development of the theory concerns its application to the Steiner tree problem and other minimal network problems which are related with a Eulerian formulation of the branched optimal transport. Starting from a 2016 paper by A. Marchese and myself, I will show how these problems and their variants are equivalent to a mass-minimization problem in the framework of currents with coefficients in a (suitably chosen) normed group. The variants I'm referring to include the multicommodity flow, the mailing problem and new models for robust and resilient traffic plans, as shown in a recent paper in collaboration with L. De Masi and A. Marchese.