05.06.2019 um 17:15 Uhr in 69/125
Prof. Dr. Dirk Lorenz (Technische Universität Braunschweig)
Analysis and Algorithms for Optimal Transport
How to move mass or goods from where they are to designated places in the most efficient way? This question was posed in geometrical terms by Gaspard Monge in the 18th century already. In the middle of the 20th century Leonid Kantorovich reformulated to problem in the language of measure theory and developed a solution theory (which actually earned him the Nobel prize in economics in 1975). In recent days there have been an increasing interest in the mathematics of optimal transport and computational tools have been developed which helped to make optimal transport applicable in fields like mathematical imaging, machine learning or inverse problems.
In this talk I will introduce various formulations of optimal transport problems (involving, e.g. dynamics of partial differential equations, minimization problems with static partial differential equations as constraints, linear programming, or matrix scaling). I will shortly speak about the analysis of the problems and then focus on the computational problem of developing practical algorithms.
28.05.2019 um 14:00 Uhr in Raum 69/118
CLTs for Geometric Functionals of Compact Sets
We consider a Boolean model based on an inhomogenous Poisson process of compact particles in Euclidean space. Our approach builds on the work of Hug, Last and Schulte (2016) and adapts their results to be compatible with our setting. We look at applications in network science, where aforementioned compact sets model communication ranges of wireless network participants.