Projects in Mathematics Muenster

Research area C: Models and Approximations
Unit C1: Evolution and asymptotics
Unit C2: Multi-scale phenomena and macroscopic structures
Unit C3: Interacting particle systems and phase transitions
Unit C4: Geometry-based modelling, approximation, and reduction

Further Projects
• CRC 1450 A05 - Targeting immune cell dynamics by longitudinal whole-body imaging and mathematical modelling online
• CRC 1450 A06 - Improving intravital microscopy of inflammatory cell response by active motion compensation using controlled adaptive optics online
• Mathematische Rekonstruktion und Modellierung der CAR T-Zell Verteilung in vivo in einem Tumormodell online
• SPP 1962: Non-smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization - SP: Non-smooth and non-convex optimal transport problems online
• Nonlocal Methods for Arbitrary Data Sources online

Research Interests

Research Interests

$\bullet$ Mathematical image processing.
$\bullet$ Inverse problems.
$\bullet$ Topology and shape optimisation.
$\bullet$ Approximation and optimisation methods in nonlinear spaces.
$\bullet$ Calculus of variations.

Selected Publications

Selected Publications of Benedikt Wirth

$\bullet$ B. Heeren, M. Rumpf, and B. Wirth. Variational time discretization of Riemannian splines. IMA J. Numer. Anal. (in press), drx077, 2018. doi.org/10.1093/imanum/drx077

$\bullet$ A. Brancolini, C. Rossmanith, and B. Wirth. Optimal micropatterns in 2D transport networks and their relation to image inpainting. Arch. for Ration. Mech. Anal., 228(1):279–308, 2018.

$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a shear load. Comm. Pure Appl. Math., 69(8):1572–1610, 2016.

$\bullet$ P.-A. Absil, P.-Y. Gousenbourger, P. Striewski, and B. Wirth. Differentiable piecewise- Bézier surfaces on Riemannian manifolds. SIAM J. Imaging Sci., 9(4):1788–1828, 2016.

$\bullet$ M. Elsey and B. Wirth. Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images. J. Sci. Comput., 63(1):279–306, 2015.

$\bullet$ K. Bredies, T. Pock, and B. Wirth. A convex, lower semicontinuous approximation of Euler's elastica energy. SIAM J. Math. Anal., 47(1):566–613, 2015.

$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load. Proc. R. Soc. A, 470(2170), 2014.

$\bullet$ W. Ring and B. Wirth. Optimization methods on Riemannian manifolds and their application to shape space. SIAM J. Optim., 22(2):596–627, 2012.

$\bullet$ P. Penzler, M. Rumpf, and B. Wirth. A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM Control Optim. Calc. Var., 18(1):229–258, 2012.

$\bullet$ B. Wirth, J. Gerhard, and W. Marquardt. Robust optimisation with normal vectors on critical manifolds of disturbance-induced stability loss. J. Nonlinear Sci., 21(1):57–92, 2011.

Current Publications

$\bullet$ J. Lohmann, B. Schmitzer, and B. Wirth. Formulation of branched transport as geometry optimization. arXiv e-prints, September 2021. arXiv:2109.07820.

$\bullet$ C. Clason, C. Tameling, and B. Wirth. Convex relaxation of discrete vector-valued optimization problems. arXiv e-prints, August 2021. arXiv:2108.10077.

$\bullet$ J. Braunsmann, M. Rajkovic, M. Rumpf, and B. Wirth. Learning low bending and low distortion manifold embeddings. arXiv e-prints, April 2021. arXiv:2104.13189.

$\bullet$ C. Dirks, P. Striewski, B. Wirth, A. Aalto, and A. Olguin-Olguin. A mathematical model for bleb regulation in zebrafish primordial germ cells. Mathematical Medicine and Biology: A Journal of the IMA, February 2021. doi:10.1093/imammb/dqab002.

$\bullet$ C. Clason, D. A. Lorenz, H. Mahler, and B. Wirth. Entropic regularization of continuous optimal transport problems. Journal of Mathematical Analysis and Applications, 494(1):124432, 22, February 2021. doi:10.1016/j.jmaa.2020.124432.

$\bullet$ P. Striewski and B. Wirth. Elastic 3d-2d image registration. arXiv e-prints, January 2021. arXiv:2101.03393.

$\bullet$ H. Hardering and B. Wirth. Quartic $L^p$-convergence of cubic Riemannian splines. arXiv e-prints, December 2020. arXiv:2012.08289.

$\bullet$ B. Schmitzer, K. P. Schäfers, and B. Wirth. Dynamic cell imaging in PET with optimal transport regularization. IEEE Transactions on Medical Imaging, 39(5):1626–1635, May 2020. doi:10.1109/TMI.2019.2953773.

$\bullet$ U. Böttcher and B. Wirth. Convex lifting-type methods for curvature regularization. In P. Grohs, M. Holler, and A. Weinmann, editors, Handbook of Variational Methods for Nonlinear Geometric Data, chapter 7, pages 207–233. Springer International Publishing, April 2020. doi:10.1007/978-3-030-31351-7_7.

$\bullet$ C. Dirks and B. Wirth. An adaptive finite element approach for lifted branched transport problems. arXiv e-prints, March 2020. arXiv:2003.13797.

$\bullet$ L. Ferrari, C. Dirks, and B. Wirth. Phase field approximations of branched transportation problems. Calc. Var. Partial Differential Equations, 59(1):Paper No. 37, 34, January 2020. doi:10.1007/s00526-019-1680-3.

$\bullet$ B. Heeren, M. Rumpf, M. Wardetzky, and B. Wirth. Discrete Riemannian calculus on shell space. In A. Bonito and R. Nochetto, editors, Geometric partial differential equations, volume 21 of Handbook of Numerical Analysis, pages 621–679. Elsevier, January 2020.

$\bullet$ C. Dirks, P. Striewski, B. Wirth, A. Aalto, A. Olguin-Olguin, and E. Raz. A mathematical model for cell polarization in zebrafish primordial germ cells. arXiv e-prints, December 2019. arXiv:1912.08627.

$\bullet$ A. Effland, B. Heeren, M. Rumpf, and B. Wirth. Consistent curvature approximation on Riemannian shape spaces. arXiv e-prints, December 2019. arXiv:1912.07336.

$\bullet$ A. Marchese and B. Wirth. Approximation of rectifiable 1-currents and weak- relaxation of the $h$-mass. Journal of Mathematical Analysis and Applications, 479(2):2268–2283, November 2019. doi:10.1016/j.jmaa.2019.07.059.

$\bullet$ B. Wirth. Phase field models for two-dimensional branched transportation problems. Calculus of Variations and Partial Differential Equations, 58(5):164, September 2019. doi:10.1007/s00526-019-1615-z.

$\bullet$ B. Schmitzer and B. Wirth. Dynamic models of Wasserstein-1-type unbalanced transport. ESAIM, 25(23):54, July 2019. doi:10.1051/cocv/2018017.

$\bullet$ C. Clason, D. A. Lorenz, H. Mahler, and B. Wirth. Entropic regularization of continuous optimal transport problems. arXiv e-prints, June 2019. arXiv:1906.01333.

$\bullet$ B. Wirth. Green's function for Poisson's equation and the EEG equation with Neumann boundary condition on $n$-balls. arXiv e-prints, February 2019. arXiv:1902.04130.

$\bullet$ B. Schmitzer, K. P. Schäfers, and B. Wirth. Dynamic cell imaging in PET with optimal transport regularization. arXiv e-prints, February 2019. arXiv:1902.07521.

$\bullet$ B. Schmitzer and B. Wirth. A framework for Wasserstein-1-type metrics. Journal of Convex Analysis, 26(2):353–396, 2019. URL: http://www.heldermann.de/JCA/JCA26/JCA262/jca26020.htm.

$\bullet$ D. P. Bourne, B. Schmitzer, and B. Wirth. Semi-discrete unbalanced optimal transport and quantization. arXiv e-prints, August 2018. arXiv:1808.01962.

$\bullet$ L. A. Davide Ferrari, C. Rossmanith, and B. Wirth. Phase field approximations of branched transportation problems. arXiv e-prints, May 2018. arXiv:1805.11399.