Research interests

• PDE's, variational calculus, gradient flows and Hamiltonian systems,
• Non-equilibrium thermodynamics & macroscopic fluctuation theory,
• Reacting particle systems and other jump processes on discrete spaces,
• Large deviations.

Teaching

2023 Lineare Algebra (Kleingruppenübungen).

2022 Höhere Mathematik 3.

2020 Large deviations (TU Berlin).

2018 Convex Analysis (TU Berlin).

Preprints

• D.R.M. Renger, Markov-bridge representation of ergodic large-deviation principles, arXiv:2407.00216 (2024).
• D.R.M. Renger, Macroscopic Fluctuation Theory versus large-deviation-induced GENERIC, arXiv: 2402.04092 (2024).

Peer-reviewed

• R.I.A. Patterson, D.R.M. Renger and U. Sharma, Variational Structures Beyond Gradient Flows: a Macroscopic Fluctuation-Theory Perspective, Journal of Statistical Physics 191, 18, (2024).
• D.R.M. Renger and U. Sharma, Untangling dissipative and Hamiltonian effects in bulk and boundary-driven systems, Physical Review E 108, 054123 (2023).
• N. Nüsken and D.R.M. Renger, Stein Variational Gradient Descent: many-particle and long-time asymptotics, Foundations of Data Science 5, 3, pp 286–320 (2023).
• M.A. Peletier and D.R.M. Renger, Fast reaction limits via Γ-convergence of the flux rate functional, Journal of Dynamics and Differential Equations 35, pp. 865–906 (2023).
• D.R.M. Renger and S. Schindler, Gradient flows for bounded linear evolution equations, Zeitschrift für Analysis und ihre Anwendungen 41, 1/2, pp. 229–238 (2022).
• A. Agazzi, L. Andreis, R.I. A. Patterson and D.R.M. Renger, Large deviations for Markov jump processes with uniformly diminishing rates, Stochastic Processes and their Applications 152, pp. 553-559 (2022).
• D.R.M. Renger, Anisothermal Chemical Reactions: Onsager-Machlup and Macroscopic Fluctuation Theory, Journal of Physics A: Mathematical and Theoretical 55, pp. 315001 (2022).
• D.R.M. Renger and J. Zimmer, Orthogonality of fluxes in general nonlinear reaction networks, Discrete & Continuous Dynamical Systems - S 14, 1, pp. 205-217 (2021).
• D. Gabrielli and D.R.M. Renger, Dynamical Phase Transitions for Flows on Finite Graphs, Journal of Statistical Physics 181, pp. 2353-2371 (2020).
• R.I.A. Patterson and D.R.M. Renger, Large Deviations of Jump Process Fluxes (view-only version), Mathematical Physics, Analysis and Geometry 22, 21 (2019).
• M. Heida, R.I.A. Patterson and D.R.M. Renger, Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space (view-only version), Journal of Evolution Equations 19, 1 (2019).
• D.R.M. Renger, Gradient and GENERIC systems in the space of fluxes, applied to reacting particle systems, Entropy, special issue "Probability Distributions and Maximum Entropy in Stochastic Chemical Reaction Networks" 20, 8 (2018).  (See also Oberwolfach report).
• D.R.M. Renger, Flux large deviations of independent and reacting particle systems, with implications for Macroscopic Fluctuation Theory, Journal of Statistical Physics 172, 5 (2018).
• P. Koltai and D.R.M. Renger, From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data, Journal of Nonlinear Science 28, 5 (2018).
• A. Mielke, R.I.A. Patterson, M.A. Peletier and D.R.M. Renger, Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics, SIAM Journal on Applied Mathematics 77, 4 (2017).
• M. Liero, A. Mielke, M.A. Peletier and D.R.M. Renger, On microscopic origins of generalized gradient structures, Discrete and Continuous Dynamical Systems - Series S 10, 1 (2017).
• A. Mielke, M. A. Peletier, and D.R.M. Renger, A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility, Journal of Non-Equilibrium Thermodynamics 41, 2 (2016).
• M. Erbar, J. Maas and D.R.M. Renger, From large deviations to Wasserstein gradient flows in multiple dimensions, Electronic Communications in Probability 20, 89 (2015).
• A. Mielke, M. A. Peletier, D.R.M. Renger, On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion, Potential Analysis 41, 4 (2014).
• M. Duong, V. Laschos and M. Renger, Wasserstein gradient flows from large deviations of many-particle limits, ESAIM: Control, Optimisation and Calculus of Variations 19, 4 (2013).
• M.A. Peletier, D.R.M. Renger and M. Veneroni, Variational formulation of the Fokker-Planck equation with decay: a particle approach, Communications in Contemporary Mathematics 15, 5 (2013).
• J.H.M. Evers, D. Kiss, W. Kowalczyk, T. Navilarekallu, M. Renger, L. Sella, V. Timperio, A. Viorel, A.C.C. van Wijk and A.N. Yzelman, Node counting in wireless ad-hoc networks, Proceedings of the 79th European Study Group Mathematics with Industry, Amsterdam (2012).

PhD thesis

• D.R.M. Renger, Microscopic interpretation of Wasserstein gradient flows, Technische Universiteit Eindhoven (2013).

Collaboration engineering

I brielfy studied (non-mathematical) topics in "collaboration engineering", resulting in the following articles and proceedings.

• M. Renger and J. Honig, Improving the quality of business process models through separation of generation tasks in collaborative modelling, International Journal of Organisational Design and Engineering 2 (2012).
• M. Renger, G.L. Kolfschoten and G.J. de Vreede, Challenges in collaborative modeling: a literature review and research agenda, International Journal of Simulation and Process Modelling 4 (2008).
• A.S. Read, M. Renger, R.O. Briggs and G.J. de Vreede, Fundamental topics of organizing: a research agenda, Proceedings of the 42nd Hawaiian International Conference on System Sciences, Los Alamitos, CA, USA (2009).
• M. Renger, G.L. Kolfschoten and G.J. de Vreede, Using interactive whiteboard technology to support collaborative modeling, Groupware: Design, Implementation, and Use - 14th International Workshop (CRIWG), Omaha, NE, USA (2008).
• M. Renger, G.L. Kolfschoten and G.J. de Vreede, Challenges in collaborative modeling: a literature review, Lecture Notes in Business Information Processing: Advances in Enterprise Engineering I, Berlin/Heidelberg, Germany (2008).
• M. Renger, G.L. Kolfschoten and G.J. de Vreede, Patterns in collaborative modeling: a literature review, Proceedings of Group Decision & Negotiation, Coimbra, Portugal (2008).

Popular Science

• "Schallwellen in elektronischer Musik", Tag der Mathematik, Beuth Hochschule, Berlin, Germany (2019).
• "Was sind und was sollen die Zahlen?", Tag der Mathematik, Universität Regensburg, Regensburg, Germany (2017).
• "Wie man nicht-differenzierbare Funktionen differenzieren kann", Tag der Mathematik, Humboldt-Universität, Berlin, Germany (2017).
• "The truth is out there... it's called math!", Nerd Nite Greatest Hits - Five years of Talks and Beers, Felix Meritis, Amsterdam, the Netherlands (2016).
• "Minimierung in unendlich vielen Dimensionen", Tag der Mathematik, Beuth Hochschule, Berlin, Germany (2015).
• "Infinity: imagining the unimaginable", Nerd Nite XVII, Crea Muziekzaal, Amsterdam, the Netherlands (2014):

• "Die Entropie von unendlich vielen Molekülen", Tag der Mathematik, Technische Universität, Berlin, Germany (2014).
• "Unendlichtkeit", 14. Lange Nacht der Wissenschaften, Geschäftsstelle der Leibniz-Gemeinschaft, Berlin, Germany (2014).