I am a Postdoctoral Fellow of the Japan Society for the Promotion of Science (JSPS) at the Department of Mathematics, Institute of Science Tokyo.
March 10-11 I visited the workshop “Geometric Analysis and Related Topics” at Kyoto University.
February 21 My talk “Dynamic inverse problems with temporal discontinuities in the Wasserstein- space” has been accepted for the conference “Curves and Surfaces” at the Le Grand Large - Palais des Congrès de Saint-Malo (in June 8-12).
February 16-20 I visited the second week of the conference “Analysis, Geometry and Probability on Metric Spaces” at Fukuoka University.
January 19-21 I gave a talk at the “Finland-Japan Workshop in Industrial and Applied Mathematics” at Josai University.
January 12-16 I visited the “Analysis on Metric Spaces Unit” at Okinawa Institute of Science and Technology and gave a talk in the “Analysis on Metric Spaces seminar”.
1) Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. “Formulation of branched transport as geometry optimization”. In: J. Math. Pures Appl. 163 (2022), pp. 739–779. Preprint VoR
2) Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. “Duality in branched transport and urban planning”. In: Appl. Math. Optim. 86 (2022), Article No. 45. Preprint VoR
3) Julius Lohmann. “On the branched transport problem. Reformulation as geometry optimization and calibration using convex duality”. Dissertation. University of Münster (2023).
4) Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. “Formulas for the -mass on -currents with coefficients in ”. In: Calc. Var. Partial Differential Equations 64 (2025), Article No. 288. Preprint VoR
5) Marcello Carioni and Julius Lohmann. “Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation”. In: Inverse Problems 41 (2025), Article No. 115018. Preprint VoR
6) Mauro Bonafini, Julius Lohmann, Olga Minevich, Bernhard Schmitzer, and Benedikt Wirth. “Optimal transport networks and their duals”. In: Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, Part II (Eds.: M. Hintermüller et al.). Internat. Ser. Numer. Math. 173 (2026). Birkhäuser. To appear.
My main research area is the field of optimal transport, in particular branched transport, multi-material transport, and generalizations of Wasserstein- transport. Currently, I study geometric flows of normal -currents (with Yoshihiro Tonegawa), a variant of the so-called urban planning problem (with Jun Kitagawa and Asuka Takatsu), and a superposition principle for unbalanced Wasserstein--type models (with Marcello Carioni).
I mainly apply or further develop methods from the calculus of variations, (convex) optimization, and (geometric) measure theory.
In the future, I would like to expand my research in the directions (geometric) evolutionary problems and optimal transport on metric spaces (using time-dependent probability measures or metric normal -currents) and Wasserstein- gradient flow theory applied to transport PDEs. I am also interested in applications to (dynamic) inverse problems and machine learning.
2011–2014 BSc Mathematics (minor Computer Science), University of Erlangen–Nuremberg
2014–2017 MSc Mathematics (minor Computer Science), University of Erlangen–Nuremberg
2015–2016 Erasmus+ semester abroad, Stockholm University
2017–2019 Half-time position (mathematics consultation hours), additional lectures in Mathematics and Computer Science, University of Erlangen–Nuremberg; field hockey coach (at NHTC in Nuremberg)
2019–2023 PhD Mathematics (Dr. rer. nat.), University of Münster, supervisor: Benedikt Wirth
2020 One-month NoMADS secondment, University of Twente, host: Michel J.A.M. van Putten
2022 Two-month NoMADS secondment, University of Cambridge, host: Carola Schönlieb
2023–2024 Postdoctoral researcher, University of Münster, host: Benedikt Wirth
2024–2024 Postdoctoral researcher, University of Helsinki, host: Tuomo Valkonen
2024–2026 Postdoctoral Fellow of the Japan Society for the Promotion of Science, Institute of Science Tokyo, host: Yoshihiro Tonegawa