I am a Postdoctoral Fellow of the Japan Society for the Promotion of Science (JSPS) at the Department of Mathematics, Institute of Science Tokyo. Beginning in December, I will hold an appointment as a Project Assistant Professor in the Department of Mathematics at Keio University, with the appointment continuing through March 31, 2027.
August 19-21 I visited the “Mathematics & AI Symposium” at RIKEN AIP Nihonbashi.
August 7 I visited the “RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences” at RIKEN Wako Campus.
July 14 I have accepted a position as a Project Assistant Professor at Keio University.
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”.
1) Julius Lohmann and Yoshihiro Tonegawa. “Geometric flows of branched transportation networks”. 2026. Preprint
2) 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.
3) 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
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) Julius Lohmann. “On the branched transport problem. Reformulation as geometry optimization and calibration using convex duality”. Dissertation. University of Münster (2023).
6) 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
7) 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
My main research area is the field of optimal transport, in particular branched transport, multi-material transport, and generalizations of Wasserstein- transport.
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.
2024–2026 Postdoctoral Fellow of the Japan Society for the Promotion of Science, Institute of Science Tokyo, host: Yoshihiro Tonegawa
2024–2024 Postdoctoral researcher, University of Helsinki, host: Tuomo Valkonen
2023–2024 Postdoctoral researcher, University of Münster, host: Benedikt Wirth
2022 Two-month NoMADS secondment, University of Cambridge, host: Carola Schönlieb
2020 One-month NoMADS secondment, University of Twente, host: Michel J.A.M. van Putten
2019–2023 PhD Mathematics (Dr. rer. nat.), University of Münster, supervisor: Benedikt Wirth
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)
2015–2016 Erasmus+ semester abroad, Stockholm University
2014–2017 MSc Mathematics (minor Computer Science), University of Erlangen–Nuremberg
2011–2014 BSc Mathematics (minor Computer Science), University of Erlangen–Nuremberg