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Technische Universität München
Technische Universität München

Picture of Johannes Zimmer

Prof. Dr. rer. nat. Johannes Zimmer

Technical University of Munich

Chair of Analysis and Modelling (Prof. Zimmer)

Postal address

Postal:
Boltzmannstr. 3
85748 Garching b. München

Research interests

  • Mathematical Modelling
  • Applied Analysis: differential equations, variational problems
  • Stochastic models and scale-bridging
  • Nonequilibrium problems

Publications

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2023

  • Brokate, Martin; Zimmer, Johannes; Lindemann, Florian: Analysis 1. Springer Spektrum, 2023 mehr… BibTeX Volltext ( DOI )
  • Huang, Shenglin; He, Zequn; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia: Statistical-Physics-Informed Neural Networks (Stat-PINNs): A Machine Learning Strategy for Coarse-graining Dissipative Dynamics. 2023 mehr… BibTeX
  • Huang, Shenglin; He, Zequn; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia: Statistical-Physics-Informed Neural Networks (Stat-PINNs): A Machine Learning Strategy for Coarse-graining Dissipative Dynamics. 2023 mehr… BibTeX

2022

  • Duong, Manh Hong; Zimmer, Johannes: On decompositions of non-reversible processes. , 2022MMSC 2022 mehr… BibTeX
  • Klar, Matthias; Matthies, Karsten; Zimmer, Johannes: Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system. Lett. Math. Phys. 112 (6), 2022, Paper No. 119, 32 mehr… BibTeX Volltext ( DOI )

2021

  • Cornalba, Federico; Shardlow, Tony; Zimmer, Johannes: Well-posedness for a regularised inertial Dean-Kawasaki model for slender particles in several space dimensions. J. Differential Equations 284, 2021, 253--283 mehr… BibTeX Volltext ( DOI )
  • Feng, Jin; Mikami, Toshio; Zimmer, Johannes: A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation. Comm. Math. Phys. 385 (1), 2021, 1--54 mehr… BibTeX Volltext ( DOI )
  • Klar, Matthias; Matthies, Karsten; Reina, Celia; Zimmer, Johannes: Second-order fast-slow dynamics of non-ergodic Hamiltonian systems: thermodynamic interpretation and simulation. Phys. D 428, 2021, Paper No. 133036, 32 mehr… BibTeX Volltext ( DOI )
  • Renger, D. R. Michiel; Zimmer, Johannes: Orthogonality of fluxes in general nonlinear reaction networks. Discrete Contin. Dyn. Syst. Ser. S 14 (1), 2021, 205--217 mehr… BibTeX Volltext ( DOI )

2020

  • Cornalba, Federico; Shardlow, Tony; Zimmer, Johannes: From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity 33 (2), 2020, 864--891 mehr… BibTeX Volltext ( DOI )
  • Huang, Shenglin; Aguado-Montero, Santiago; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia: From Particle Fluctuations to Macroscopic Evolution Equations: The Case of Exclusion Dynamics. Mathematical Modeling and Scientific Computing: Focus on Complex Processes and Systems 2020, 2020 mehr… BibTeX
  • Schwetlick, Hartmut; Sutton, Daniel C.; Zimmer, Johannes: Effective Hamiltonian dynamics via the Maupertuis principle. Discrete Contin. Dyn. Syst. Ser. S 13 (4), 2020, 1395--1410 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: On fluctuations in particle systems and their links to macroscopic models. Oberwolfach Rep. 17 (2/3), 2020, 1421--1424 mehr… BibTeX

2019

  • Ansini, Nadia; Braides, Andrea; Zimmer, Johannes: Minimizing movements for oscillating energies: the critical regime. Proc. Roy. Soc. Edinburgh Sect. A 149 (3), 2019, 719--737 mehr… BibTeX Volltext ( DOI )
  • Buffoni, Boris; Schwetlick, Hartmut; Zimmer, Johannes: Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential. J. Math. Pures Appl. (9) 123, 2019, 1--40 mehr… BibTeX Volltext ( DOI )
  • Cornalba, Federico; Shardlow, Tony; Zimmer, Johannes: A regularised Dean-Kawasaki model: derivation and analysis. SIAM J. Math. Anal. 51 (2), 2019, 1137--1187 mehr… BibTeX Volltext ( DOI )
  • Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes: A variational structure for interacting particle systems and their hydrodynamic scaling limits. Commun. Math. Sci. 17 (3), 2019, 739--780 mehr… BibTeX Volltext ( DOI )
  • Li, Xiaoguai; Dirr, Nicolas; Embacher, Peter; Zimmer, Johannes; Reina, Celia: Harnessing fluctuations to discover dissipative evolution equations. J. Mech. Phys. Solids 131, 2019, 240--251 mehr… BibTeX Volltext ( DOI )

2018

  • Duhart, Horacio González; Mörters, Peter; Zimmer, Johannes: The semi-infinite asymmetric exclusion process: large deviations via matrix products. Potential Anal. 48 (3), 2018, 301--323 mehr… BibTeX Volltext ( DOI )
  • Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia: Computing diffusivities from particle models out of equilibrium. Proc. A. 474 (2212), 2018, 20170694, 21 mehr… BibTeX Volltext ( DOI )
  • Guo, Shangjiang; Zimmer, Johannes: Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects. Bull. Malays. Math. Sci. Soc. 41 (2), 2018, 919--943 mehr… BibTeX Volltext ( DOI )
  • Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes: Canonical structure and orthogonality of forces and currents in irreversible Markov chains. J. Stat. Phys. 170 (6), 2018, 1019--1050 mehr… BibTeX Volltext ( DOI )

2017

  • Buffoni, Boris; Schwetlick, Hartmut; Zimmer, Johannes: Travelling waves for a Frenkel-Kontorova chain. J. Differential Equations 263 (4), 2017, 2317--2342 mehr… BibTeX Volltext ( DOI )
  • Dirr, Nicolas; Stamatakis, Marios G.; Zimmer, Johannes: Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles. J. Stat. Phys. 168 (4), 2017, 794--825 mehr… BibTeX Volltext ( DOI )
  • Hömberg, Dietmar; Patacchini, Francesco Saverio; Sakamoto, Kenichi; Zimmer, Johannes: A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel. IMA J. Appl. Math. 82 (4), 2017, 763--780 mehr… BibTeX Volltext ( DOI )
  • Jack, Robert L.; Kaiser, Marcus; Zimmer, Johannes: Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics. Entropy 19 (10), 2017, 562 mehr… BibTeX Volltext ( DOI )
  • Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes: Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance. J. Stat. Phys. 168 (2), 2017, 259--287 mehr… BibTeX
  • Zimmer, Johannes: On fluctuations in Markov chains. Oberwolfach Reports 14 (4), 2017, 3242--3245 mehr… BibTeX

2016

  • Dirr, Nicolas; Stamatakis, Marios; Zimmer, Johannes: Entropic and gradient flow formulations for nonlinear diffusion. J. Math. Phys. 57 (8), 2016, 081505, 13 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, Hartmut; Zimmer, Johannes: A convergent string method: Existence and approximation for the Hamiltonian boundary-value problem. In: Hagen, Thomas; Rupp, Florian; Scheurle, Jürgen (Hrsg.): World Scientific, 2016 mehr… BibTeX

2015

  • Betz, Volker; König, Wolfgang; Theil, Florian; Zimmer, Johannes: Introduction, Workshop \emphInterplay of Analysis and Probability in Applied Mathematics. Oberwolfach Rep. 12 (3), 2015, 1989--1991 mehr… BibTeX
  • Guo, Shangjiang; Zimmer, Johannes: Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects. Nonlinearity 28 (2), 2015, 463--492 mehr… BibTeX Volltext ( DOI )
  • Reina, Celia; Zimmer, Johannes: Entropy production and the geometry of dissipative evolution equations. Phys. Rev. E 92 (5), 2015, 052117, 7 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, Hartmut; Sutton, Daniel C.; Zimmer, Johannes: The Finsler metric obtained as the $Γ$-limit of a generalised Manhattan metric. J. Convex Anal. 22 (1), 2015, 19--36 mehr… BibTeX
  • Schwetlick, Hartmut; Sutton, Daniel C.; Zimmer, Johannes: On the $Γ$-limit for a non-uniformly bounded sequence of two-phase metric functionals. Discrete Contin. Dyn. Syst. 35 (1), 2015, 411--426 mehr… BibTeX

2014

  • Duong, Manh Hong; Peletier, Mark A.; Zimmer, Johannes: Conservative-dissipative approximation schemes for a generalized Kramers equation. Math. Methods Appl. Sci. 37 (16), 2014, 2517--2540 mehr… BibTeX Volltext ( DOI )
  • Jack, Robert L.; Zimmer, Johannes: Geometrical interpretation of fluctuating hydrodynamics in diffusive systems. J. Phys. A 47 (48), 2014, 485001, 17 mehr… BibTeX Volltext ( DOI )
  • Venney, Christine R.; Zimmer, Johannes: Travelling lattice waves in a toy model of Lennard-Jones interaction. Quart. Appl. Math. 72 (1), 2014, 65--84 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: From particles to a conservation law: large deviations for the totally asymmetric exclusion process on the half line. Oberwolfach Rep. 11 (4), 2014, 3188--3190 mehr… BibTeX

2013

  • Adams, Stefan; Dirr, Nicolas; Peletier, Mark; Zimmer, Johannes: Large deviations and gradient flows. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 371 (2005), 2013, 20120341, 17 mehr… BibTeX Volltext ( DOI )
  • Das, Amit; Acharya, Amit; Matthies, Karsten; Zimmer, Johannes: Can equations of equilibrium predict all physical equilibria? A case study from Field Dislocation Mechanics. Math. Mech. Solids 18 (8), 2013, 803--822 mehr… BibTeX
  • Duong, Manh Hong; Peletier, Mark A.; Zimmer, Johannes: GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles. Nonlinearity 26 (11), 2013, 2951--2971 mehr… BibTeX Volltext ( DOI )
  • Herrmann, Michael; Matthies, Karsten; Schwetlick, Hartmut; Zimmer, Johannes: Subsonic phase transition waves in bistable lattice models with small spinodal region. SIAM J. Math. Anal. 45 (5), 2013, 2625--2645 mehr… BibTeX Volltext ( DOI )
  • Kružík, Martin; Zimmer, Johannes: Modelling of thin martensitic films with nonpolynomial stored energies. In: Recent trends in dynamical systems. Springer, Basel, 2013, 587--608 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, H.; Zimmer, J.: The computation of long time Hamiltonian trajectories for molecular systems via global geodesics. In: Numerical mathematics and advanced applications 2011. Springer, Heidelberg, 2013, 227--234 mehr… BibTeX
  • Zimmer, Johannes: From simple particle models to GENERIC. Oberwolfach Rep. 10 (4), 2013, 3182--3184 mehr… BibTeX

2012

  • Dirr, Nicolas; Laschos, Vaios; Zimmer, Johannes: Upscaling from particle models to entropic gradient flows. J. Math. Phys. 53 (6), 2012, 063704, 9 mehr… BibTeX Volltext ( DOI )
  • Herrmann, Michael; Schwetlick, Hartmut; Zimmer, Johannes: On selection criteria for problems with moving inhomogeneities. Contin. Mech. Thermodyn. 24 (1), 2012, 21--36 mehr… BibTeX Volltext ( DOI )
  • Kružík, Martin; Zimmer, Johannes: Rate-independent processes with linear growth energies and time-dependent boundary conditions. Discrete Contin. Dyn. Syst. Ser. S 5 (3), 2012, 591--604 mehr… BibTeX Volltext ( DOI )
  • Kružík, Martin; Zimmer, Johannes: On an extension of the space of bounded deformations. Z. Anal. Anwend. 31 (1), 2012, 75--91 mehr… BibTeX Volltext ( DOI )
  • König, Wolfgang; Mörters, Peter; Peletier, Mark A.; Zimmer, Johannes: Introduction, Workshop \emphInterplay of analysis and probability in physics. Oberwolfach Rep. 9 (1), 2012, 281--283 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, Hartmut; Sutton, Daniel C.; Zimmer, Johannes: Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model. J. Nonlinear Sci. 22 (6), 2012, 917--934 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, Hartmut; Zimmer, Johannes: Kinetic relations for a lattice model of phase transitions. Arch. Ration. Mech. Anal. 206 (2), 2012, 707--724 mehr… BibTeX Volltext ( DOI )

2011

  • Adams, Stefan; Dirr, Nicolas; Peletier, Mark A.; Zimmer, Johannes: From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage. Comm. Math. Phys. 307 (3), 2011, 791--815 mehr… BibTeX Volltext ( DOI )
  • Kreiner, Carl-Friedrich; Zimmer, Johannes: Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential. Nonlinearity 24 (4), 2011, 1137--1163 mehr… BibTeX Volltext ( DOI )
  • Kružík, Martin; Zimmer, Johannes: A model of shape memory alloys taking into account plasticity. IMA J. Appl. Math. 76 (1), 2011, 193--216 mehr… BibTeX Volltext ( DOI )
  • Kundin, Julia; Emmerich, Heike; Zimmer, Johannes: Mathematical concepts for the micro-mechanical modeling of dislocation dynamics with a phase-field approach. Phil. Mag. 91 (1), 2011, 97--121 mehr… BibTeX Volltext ( DOI )
  • Venney, Christine R.; Zimmer, Johannes: Persistence of supersonic periodic solutions for chains with anharmonic interaction potentials between neighbours and next to nearest neighbours. Dyn. Syst. 26 (4), 2011, 503--518 mehr… BibTeX Volltext ( DOI )

2010

  • Acharya, Amit; Matthies, Karsten; Zimmer, Johannes: Travelling wave solutions for a quasilinear model of field dislocation mechanics. J. Mech. Phys. Solids 58 (12), 2010, 2043--2053 mehr… BibTeX Volltext ( DOI )
  • Kružík, Martin; Zimmer, Johannes: Evolutionary problems in non-reflexive spaces. ESAIM Control Optim. Calc. Var. 16 (1), 2010, 1--22 mehr… BibTeX Volltext ( DOI )
  • Kundin, Julia; Emmerich, Heike; Zimmer, Johannes: Three-dimensional model of martensitic transformations with elasto-plastic effects. Phil. Mag. 90 (11), 2010, 1495--1510 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: A variational approach to the Hamiltonian boundary value problem: existence and approximation. Oberwolfach Rep. 7 (1), 2010, 792--794 mehr… BibTeX

2009

  • Babych, Natalia; Zimmer, Johannes: Asymptotics of resonances in a thermoelastic model with light local mass perturbations. Quart. Appl. Math. 67 (2), 2009, 311--326 mehr… BibTeX
  • Chenchiah, Isaac Vikram; Rieger, Marc Oliver; Zimmer, Johannes: Gradient flows in asymmetric metric spaces. Nonlinear Anal. 71 (11), 2009, 5820--5834 mehr… BibTeX Volltext ( DOI )
  • Dondl, Patrick W.; Hormann, Kai; Zimmer, Johannes: Modeling transformation paths of multiphase materials: The triple point of zirconia. Phys. Rev. B 79 (10), 2009, 104114, 12 mehr… BibTeX Volltext ( DOI )
  • Kreiner, Carl-Friedrich; Zimmer, Johannes: Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction. Discrete Contin. Dyn. Syst. 25 (3), 2009, 915--931 mehr… BibTeX Volltext ( DOI )
  • Kreiner, Carl-Friedrich; Zimmer, Johannes: Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction. Nonlinear Anal. 70 (9), 2009, 3146--3158 mehr… BibTeX Volltext ( DOI )
  • Rieger, Marc Oliver; Zimmer, Johannes: Young measure flow as a model for damage. Z. Angew. Math. Phys. 60 (1), 2009, 1--32 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, Hartmut; Zimmer, Johannes: Existence of dynamic phase transitions in a one-dimensional lattice model with piecewise quadratic interaction potential. SIAM J. Math. Anal. 41 (3), 2009, 1231--1271 mehr… BibTeX Volltext ( DOI )
  • Schwetlick, Hartmut; Zimmer, Johannes: Calculation of long time classical trajectories: Algorithmic treatment and applications for molecular systems. J. Chem. Phys. 130 (12), 2009, 124106, 11 mehr… BibTeX Volltext ( DOI )

2008

  • Mörters, Peter; Moser, Roger; Penrose, Mathew; Schwetlick, Hartmut; Zimmer, Johannes (Hrsg.): Analysis and stochastics of growth processes and interface models. Oxford University Press, Oxford, 2008 mehr… BibTeX Volltext ( DOI )
  • König, Wolfgang; Mörters, Peter; Zimmer, Johannes: Introduction, Workshop \emphInterplay of analysis and probability in physics. Oberwolfach Rep. 5 (4), 2008, 3065--3066 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: Travelling waves in atomistic chains and kinetic relations. Oberwolfach Rep. 5 (2), 2008, 1092--1094 mehr… BibTeX

2007

  • Catto, Isabelle; Chenchiah, Isaac Vikram; Veselić, Ivan; Zimmer, Johannes: Introduction, Miniworkshop \emphMultiscale and Variational Methods in Material Science and Quantum Theory of Solids. Oberwolfach Rep. 4 (1), 2007, 371--372 mehr… BibTeX
  • Collins, Julia; Zimmer, Johannes: An asymmetric Arzelà-Ascoli theorem. Topology Appl. 154 (11), 2007, 2312--2322 mehr… BibTeX
  • Hormann, Kai; Zimmer, Johannes: On Landau theory and symmetric energy landscapes for phase transitions. J. Mech. Phys. Solids 55 (7), 2007, 1385--1409 mehr… BibTeX
  • Schwetlick, Hartmut; Zimmer, Johannes: Solitary waves for nonconvex FPU lattices. J. Nonlinear Sci. 17 (1), 2007, 1--12 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: Discrete dynamic models for phase transitions. Oberwolfach Rep. 4 (1), 2007, 391--392 mehr… BibTeX
  • Zimmer, Johannes: Evolutionary problems with energies with linear growth. Oberwolfach Rep. 4 (1), 2007, 655--657 mehr… BibTeX
  • Zimmer, Johannes: Travelling waves in atomic models for phase-transforming materials and kinetic relations. Oberwolfach Rep. 4 (2), 2007, 1642--1645 mehr… BibTeX

2006

  • Kreiner, Carl-Friedrich; Zimmer, Johannes: Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices. ESAIM Control Optim. Calc. Var. 12 (2), 2006, 253--270 (electronic) mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: Review of \emphVariational and Extremum Principles in Macroscopic Systems, Stanislaw Sieniutycz and Henrik Farkas (eds). J. Phys. A: Math. Gen. 39 (14), 2006, 3851--3852 mehr… BibTeX
  • Zimmer, Johannes: Jog my shape memory: dynamics as a challenge in mathematical materials science. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 364 (1849), 2006, 3285--3300 mehr… BibTeX

2005

  • Rieger, Marc Oliver; Zimmer, Johannes: Global existence for nonconvex thermoelasticity. Adv. Math. Sci. Appl. 15 (2), 2005, 559--569 mehr… BibTeX

2004

  • Bhattacharya, Kaushik; Conti, Sergio; Zanzotto, Giovanni; Zimmer, Johannes: Crystal symmetry and the reversibility of martensitic transformations. Nature 428 (6978), 2004, 55--59 mehr… BibTeX
  • Dondl, Patrick W.; Zimmer, Johannes: Modeling and simulation of martensitic phase transitions with a triple point. J. Mech. Phys. Solids 52 (9), 2004, 2057--2077 mehr… BibTeX Volltext ( DOI )
  • Kreiner, Carl-Friedrich; Zimmer, Johannes; Chenchiah, Isaac: Towards the efficient computation of effective properties of microstructured materials. C. R. Mecanique 332 (3), 2004, 169--174 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: Dynamical problems with nonconvex energies as a model of damage in materials. Oberwolfach Rep. 1 (3), 2004, 1650--1652 mehr… BibTeX
  • Zimmer, Johannes: Stored energy functions for phase transitions in crystals. Arch. Ration. Mech. Anal. 172 (2), 2004, 191--212 mehr… BibTeX Volltext ( DOI )
  • Zimmer, Johannes: Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy. J. Math. Anal. Appl. 292 (2), 2004, 589--604 mehr… BibTeX Volltext ( DOI )

2003

  • Schleicher, Dierk; Zimmer, Johannes: Periodic points and dynamic rays of exponential maps. Ann. Acad. Sci. Fenn. Math. 28 (2), 2003, 327--354 mehr… BibTeX
  • Schleicher, Dierk; Zimmer, Johannes: Escaping points of exponential maps. J. London Math. Soc. (2) 67 (2), 2003, 380--400 mehr… BibTeX Volltext ( DOI )

2000

  • Zimmer, Johannes: Mathematische Modellierung und Analyse von Formgedächtnislegierungen in mehreren Raumdimensionen (Mathematical Modeling and Analysis of Shape Memory Alloys in Several Space Dimensions). Dissertation, 2000 mehr… BibTeX

1997

  • Zimmer, Johannes: Über das Iterationsverhalten von postsingulär endlichen Exponentialabbildungen (On the Iteration of Postsingularly Finite Exponential Maps). , 1997 mehr… BibTeX

Teaching

Winter term 2023/24

TitleDatesLecturer (assistant)
Analysis 3 (Central Exercise) [MA0003]Link
Analysis 3 (Exercise Session) [MA0003]Link
Analysis 3 [MA0003]Link
Seminar on Mathematical ModellingLink
Seminar on Topics in NonequilibriumLink

Summer term 2024

TitleDatesLecturer (assistant)
Calculus: Differentiation and Integration (Exercise Session) [MA9802]Link
Calculus: Differentiation and Integration [MA9802]Link
Doktorandenseminar JADS - Mathematics of InformationLink
Seminar on Mathematical ModellingLink
Seminar on Topics in NonequilibriumLink
Workshop (Counterexamples in Analysis) [MA0006P]Link

A list of previous courses can be found on TUMonline.

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