Tuesday, 13 March 2018, 3 p.m. (sharp),
Dr. Andrea Marchese, Università degli studi di Pavia
at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
Stability and new techniques in branched transportation.
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
In many natural mass transportation systems there is a certain convenience in grouping together some mass particles during the transportation process, which is typically originating branched structures. This behaviour is evident e.g. in the structure of the nerves of a leaf, the branches and the roots of a tree, or the nervous, the bronchial, and the cardiovascular system. Mathematically, this is modeled introducing a transportation cost which is proportional to a fractional power of the mass flow along the network created by the particles' trajectories.
In this talk I will describe some new results on the stability of minimizers of branched transportation problems with respect to variations of the given datum (i.e. a pair of distributions of particles to be transported one onto the other). I will also describe a new formulation of the discrete problem which allows to introduce a notion of calibration in this context: a tool from the theory of minimal surfaces which allows to prove the minimality of a concrete configuration.
Based on joint works with M. Colombo, A. De Rosa, A. Massaccesi, S. Stuvard, and R. Tione.