- Stochastic particle systems, large deviations and statistical mechanics
- Chemical reactions, coagulation, fragmentation and the Smoluchowski equation
- PDE's, variational calculus and gradient structures
I'm now teaching convex analysis
at the TU Berlin. The lecture notes and exercises can be found here
- Lecture notes 1 with exercises,
- Lecture notes 2 with exercises,
- Lecture notes 3 with exercises,
- Lecture notes 4 with exercises,
- Lecture notes 5 with exercises,
- Lecture notes 6 with exercises,
- Lecture notes 7 with exercises,
- Lecture notes 8 with exercises,
- Lecture notes 9 with exercises,
- Lecture notes 10 with exercises,
- Lecture notes 11 with exercises,
- Lecture notes 12 with exercises,
- Lecture notes 13 with exercises.
About the exam: I will not
- Linear functional analysis,
- Gradient flows,
- Moreau-Yosida regularisation (possibly only the definition & main idea),
- Lower semicontinuity of Lagrangian actions (possibly only the result),
- Poly-, quasi- and rank-one convexity,
- Every detail of every proof.
I may ask about:
- Proof strategies (Hahn-Banach, sup over cont. affine functions, etc.),
- The direct method (main idea and how to apply it),
- Interplay between convexity, topology and (lower semi) continuity,
- Epigraphs, subdifferentials, envelopes,
- Convex duality (particularly examples and calculus of convex duals!),
- Convex inequalities ((sub)gradient inequality, monotonicity, pos. semidefiniteness of 2nd derivatives and differentiability),
- Jensen's inequality and how to use it,
- Uniform integrability (not too detailed though),
- Orlicz and Mφ spaces with the Luxemburg and Orlicz norms, their (pre)dual, the Δ2-property.
In general, practice by doing the exercises!
- 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), 596 (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, Online first, (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 (Online first) (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).
Publications (collaboration engineering)
In 2008, I researched topics in "collaboration engineering" at the Systems Engineering Section
of the TU Delft. Click here to show/hide these publications
- 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
- 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.