I am a Postdoctoral Fellow of the Japan Society for the Promotion of Science (JSPS) at the Department of Mathematics, Institute of Science Tokyo.
June 24-26 I visited the “Bayes-Duality Workshop” at RIKEN AIP Nihonbashi.
June 8-12 I visited the conference “Curves and Surfaces” at Palais du Grand Large in Saint-Malo and gave a talk in the mini-symposium “Inverse problems”.
May 8-11 I visited the conference “JAMI” at Shonan Village Center.
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.
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