| Private Homepage | https://www.uni-muenster.de/Stochastik/Arbeitsgruppen/Huesmann/ |
| Research Interests | optimal transport stochastic analysis random measures, point processes stochastic mass transfer, martingale optimal transport, causal transport matching and allocation problems robust finance |
| Selected Publications | • Beiglböck M, Cox AMG, Huesmann M Optimal transport and Skorokhod embedding. Inventiones Mathematicae Vol. 208 (2), 2017, pp 327-400 online • Beiglböck M, Cox AMG, Huesmann M The geometry of multi-marginal Skorokhod Embedding. Probability Theory and Related Fields Vol. 176, 2020 online • Huesmann M, Sturm K Optimal transport from Lebesgue to Poisson. Ann. Probab. Vol. 41 (4), 2013, pp 2426-2478 online • Backhoff-Veraguas J, Beiglböck M, Huesmann M, Källblad S Martingale Benamou-Brenier: a probabilistic perspective. Ann. Probab. Vol. 48 (5), 2020 online |
| Topics in Mathematics Münster | T5: Curvature, shape, and global analysis T8: Random discrete structures and their limits |
| Current Publications | • Backhoff-Veraguas J, Beiglböck M, Huesmann M, Källblad S Martingale Benamou-Brenier: a probabilistic perspective. Ann. Probab. Vol. 48 (5), 2020 online • Beiglböck M, Cox AMG, Huesmann M The geometry of multi-marginal Skorokhod Embedding. Probability Theory and Related Fields Vol. 176, 2020 online • Huesmann M, Trevisan D A Benamou-Brenier formulation of martingale optimal transport. Bernoulli Vol. 25 (4A), 2019, pp 2729-2757 online • Huesmann M, Stebegg F Monotonicity preserving transformations of MOT and SEP. Stochastic Processes and their Applications Vol. 128 (4), 2018, pp 1114-1134 online |
| Current Projects | • EXC 2044 - C1: Evolution and asymptotics In this unit, we will use generalisations of optimal transport metrics to develop gradient flow descriptions of (cross)-diffusion-reaction systems, rigorously analyse their pattern forming properties, and develop corresponding efficient numerical schemes. Related transport-type- and hyperbolic systems will be compared with respect to their pattern-forming behaviour, especially when mass is conserved. Bifurcations and the effects of noise perturbations will be explored. Moreover, we aim to understand defect structures, their stability and their interactions. Examples are the evolution of fractures in brittle materials and of vortices in fluids. Our analysis will explore the underlying geometry of defect dynamics such as gradient descents or Hamiltonian structures. Also, we will further develop continuum mechanics and asymptotic descriptions for multiple bodies which deform, divide, move, and dynamically attach to each other in order to better describe the bio-mechanics of growing and dividing soft tissues. Finally, we are interested in the asymptotic analysis of various random structures as the size or the dimension of the structure goes to infinity. More specifically, we shall consider random polytopes and random trees.For random polytopes we would like to compute the expected number of faces in all dimensions, the expected (intrinsic) volume, and absorption probabilities, as well as higher moments and limit distributions for these quantities. online | martin dot huesmann at uni-muenster dot de |
| Phone | +49 251 83-35086 |
| FAX | +49 251 83-32712 |
| Room | 130.017 |
| Secretary | Sekretariat Stochastik Frau Yvonne (Stochastik) Stein Telefon +49 251 83-33770 Fax +49 251 83-32712 Zimmer 130.030 |
| Address | Prof. Dr. Martin Huesmann Institut für Mathematische Stochastik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |
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