- Reacting particle systems and other jump processes on discrete spaces
- Non-equilibrium thermodynamics/statistical physics, Macroscopic Fluctuation Theory
- PDE's, variational calculus and gradient structures
TeachingIn the summer 2020 I taught a course in large deviations at the TU Berlin.
In the summer 2018 I taught a course in convex analysis at the TU Berlin. Click for the (handwritten) lecture notes with exercises.
- R.I.A. Patterson, D.R.M. Renger and U. Sharma, Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective. ArXiv Preprint 2103.14384 (2021).
- N. Nüsken and D.R.M. Renger, Stein Variational Gradient Descent: many-particle and long-time asymptotics. ArXiv Preprint 2102.12956 (2021).
- A. Agazzi, L. Andreis, R.I. A. Patterson and D.R.M. Renger, Large deviations for Markov jump processes with uniformly diminishing rates ArXiv Preprint 2102.13040 (2021).
- M.A. Peletier and D.R.M. Renger, Fast reaction limits via Γ-convergence of the Flux Rate Functional. ArXiv Preprint 2009.14546 (2020).
- D. Gabrielli and D.R.M. Renger, Dynamical Phase Transitions for Flows on Finite Graphs. Journal of Statistical Physics 181, 2353-2371 (2020).
- D.R.M. Renger and J. Zimmer, Orthogonality of fluxes in general nonlinear reaction networks. Discrete & Continuous Dynamical Systems - S 14 (1), 205-217 (2021).
- R.I.A. Patterson and D.R.M. Renger, Large Deviations of Jump Process Fluxes (view-only version). Mathematical Physics, Analysis and Geometry First Online (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: D.R.M. Renger, Generalised Gradient Systems and GENERIC in Flux Space. Oberwolfach Report 1746 (2018).
- 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, the Netherlands (2012).
- D.R.M. Renger. Microscopic interpretation of Wasserstein gradient flows. Technische Universiteit Eindhoven (2013).
Publications (collaboration engineering)In 2008, I researched topics in "collaboration engineering" at the Technology, Policy and Management Department of the TU Delft. Click here to show/hide these publications.
- 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).
Organization of events
- 29 May - 2 June 2017: CRC 1114 Spring School "Methods for Particle Systems with Multiple Scales" (with A. Mielke) at WIAS, Berlin, Germany.
- 16-18 December 2015: "Stochastic Limit Analysis for Reacting Particles Systems" (with W. König and R.I.A. Patterson) at WIAS, Berlin, Germany.
- 10-14 March 2014: Young European Probabilists XI "Mass transport in analysis and probability" (with M.-K. von Renesse and P. Mörters) at Eurandom, Eindhoven, the Netherlands.
- 18-20 April 2012: ICMS Workshop "Open problems between micro and macro in systems of agents and particles" (with A. Muntean and M.A. Peletier) at Eurandom, Eindhoven, the Netherlands.
- 11 Mai 2019: "Schallwellen in elektronischer Musik", Tag der Mathematik at Beuth Hochschule, Berlin, Germany.
- 28 July 2017: "Was sind und was sollen die Zahlen?", Tag der Mathematik at Universität Regensburg, Regensburg, Germany.
- 22 April 2017: "Wie man nicht-differenzierbare Funktionen differenzieren kann", Tag der Mathematik at Humboldt-Universität, Berlin, Germany.
- 15 April 2016: "The truth is out there... it's called math!", Nerd Nite Greatest Hits - Five years of Talks and Beers at Felix Meritis, Amsterdam, the Netherlands.
- 9 May 2015: "Minimierung in unendlich vielen Dimensionen", Tag der Mathematik at Beuth Hochschule, Berlin, Germany.
- 6 June 2014: Here is my talk "Infinity: imagining the unimaginable", Nerd Nite XVII at Crea Muziekzaal, Amsterdam, the Netherlands:
- 17 May 2014: "Die Entropie von unendlich vielen Molekülen", Tag der Mathematik at Technische Universität, Berlin, Germany.
- 10 May 2014: "Unendlichtkeit", 14. Lange Nacht der Wissenschaften at Geschäftsstelle der Leibniz-Gemeinschaft, Berlin, Germany.