Publications

1. M.T. Wolfram, Semiconductor inverse dopant profiling from transient measurements , Journal of Computational Electronics, 6(4), 395-444, 2007
2. M. Burger, R. Pinnau, M.T. Wolfram, On-off-state design of semiconductor doping profiles, Commun. Math. Sci., 6, 1021-1041, 2008
3. P.A. Markowich, N. Matevosyan, J.F. Pietschmann, M.T. Wolfram, On a parabolic free boundary value problem modeling price formation , Math. Models Methods Appl. Sci., 11(19), 1929-1957, 2009
4. B. Duering, P.A. Markowich, J.F. Pietschmann, M.T. Wolfram, Boltzmann and Fokker-Planck Equations modelling Opinion Formation in the Presence of Strong Leaders , Proc. Royal Soc. A., 465(2112), 3687-3708, 2009
5. M. Burger, J.A. Carrillo, M.T. Wolfram, A mixed finite element method for nonlinear diffusion equations , KRM, 3(1), 59-83, 2010
6. M.T. Wolfram, M. Buger, Z.S. Siwy, Mathematical modeling and simulation of nanopore blocking by precipitation ,J. Phys.: Condens. Matter, 22(45), 2010
7. M. Burger, N. Matevosyan, M.T. Wolfram, A level set based shape optimization method for an elliptic obstacle problem, M3AS, 21(4), 616-649, 2011
8. M. Di Francesco, P.A. Markowich, J.F. Pietschmann, M.T. Wolfram, On the Hughes' model of pedestrian flow: The one-dimensional case, JDE, 250(3), 1334-1362, 2011
9. L.A. Caffarelli, P.A. Markowich, M.T. Wolfram, On a price formation free boundary value model by Lasry & Lions: The Neumann problem, C. R. Acad. Sci. Paris, 349, 841-844, 2011
10. A. Lachapelle, M.T. Wolfram, On a mean field game approach modeling congestion and aversion in pedestrian crowds, Trans. Res.: Part B: Methodological, 45(10), 1572-1589, 2011
11. M. Burger, B. Schlake, M.T. Wolfram, Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries, Nonlinearity, 25, 961-990, 2012
12. D. Brinkman, K. Fellner, P.A. Markowich, M.T. Wolfram, A drift-diffusion reaction model for excitonic photovoltaic bilayers: asymptotic analysis and a 2D HDG finite element scheme, M3AS., 23(5), 2013
13. M. Burger, J. Haskovec, M.T. Wolfram, Individual based and mean-field modelling of direct aggregation, Physica D: Nonlinear Phenomena, 260, 145-158, 2013
14. M. Burger, L. Cafferelli, P.A. Markowich, M.T. Wolfram, On a Boltzmann type price formation model, Proc. R. Soc. A, 469(2157), 20130126, 2013
15. M. Burger, J.F. Pietschmann, M.T. Wolfram, Identification of non-linearities in transport-diffusion models modelling crowded motion, Inverse Problems and Imaging, 7(4), 1157-1182, 2013
16. J.F. Pietschmann, M.T. Wolfram, M. Burger, C. Trautmann, G. Nguyen, M. Pevarnik, V. Bayer, Z. Siwy Rectification properties of conically shaped nanopores: consequences of miniaturization, Physical Chemistry Chemical Physics, 15, 16917-16926, 2013
17. M. Burger, M. Di Francesco, P.A. Markowich, M.T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics, Discrete and Dynamical Systems - B, 19(5), 1311-1333, 2014
18. M. Burger, L. Caffarelli, P.A. Markowich, M.T. Wolfram, On the asymptotic behavior of a Boltzmann-type price formation model, CMS, 12(7), 1353--1361, 2014
19. D. Gomes, R.M. Velho, M.T. Wolfram, Socio economic applications of finite state mean field games, Phil. Trans. R. Soc. A, 372(2028), 20130405, 2014
20. B. Duering, M.T. Wolfram, Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation, Proc Royal Soc A 471(2182), 2015
21. J. Carrillo, S. Martin, M.T. Wolfram, A local version of the Hughes model for pedestrian flow, M3AS 26(4), 671-697, 2016 Arxiv
22. M. Burger, S. Hittmeir, H. Ranetbauer, M.T. Wolfram, Lane formation by side-stepping, SIAM Math. Anal. 48(2), 981-1005, 2016 Arxiv
23. M. Burger, A. Lorz, M.T. Wolfram, On a Boltzmann type model for knowledge growth, SIAM J. Appl. Math. 76(5), 1799-1818, 2016 Arxiv
24. P.A. Markowich, J. Teichmann, M.T. Wolfram, Parabolic free boundary price formation models under market size fluctuations, SIAM MMS 14(4), 1211-1237, 2016 Arxiv
25. E. Carlini, A. Festa, F. Silva, M.T. Wolfram, A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow, Dynamic Games and Applications 7, 2016 Arxiv 
26. J. Carrillo, H. Ranetbauer, M.T. Wolfram, Numerical simulation of continuity equations by evolving diffeomorphisms, J Comput. Phys. 327, 186-202, 2016 Arxiv
27. M. Burger, A. Lorz, M.T. Wolfram, Existence of balanced growth path solutions to a Boltzmann mean field game model for knowledge growth, KRM, 10(1), 117-140, 2016 Arxiv
28. M. Bruna, M. Burger, H. Ranetbauer, M.T. Wolfram, Cross-diffusion systems with excluded-volume effects and asymptotic gradient flow structures, JNLS 27(2), 2017 Arxiv
29. B. Matejczyk, M. Valisko, M.-T. Wolfram, J.-F. Pietschmann, D. Boda, Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo, J. Chem. Phys. 146, 2017 Arxiv
30. S. Hittmeir, H. Ranetbauer, C. Schmeiser, M.T. Wolfram, Derivation and analysis of continuum models for crossing pedestrian traffic, M3AS 27, 2017 Arxiv
31. A. Festa, A. Tosin, M.T. Wolfram, Kinetic description of collision avoidance in pedestrian dynamics by sidestepping, Kinet. Relat. Math. 11(3), 2018 Arxiv
32. B. Matejczyk, J.-F. Pietschmann, G. Richardson, M.T. Wolfram, Asymptotic models for transport in large aspect ratio nanopores, EJAM 30(3) 2019 Arxiv
33. B. Duering, M. Torregrossa, M.T. Wolfram, Boltzmann and Fokker-Planck Equations Modelling the Elo Rating System with Learning Effects, JNLS 29(3), 2019 Arxiv
34. S. Gomes, A. Stuart and M.T. Wolfram, Parameter estimation for macroscopic pedestrian dynamics models from microscopic data, SIAM J. Appl. Math 79(4), 2019 Arxiv
35. A. Stuart, M.T. Wolfram, Inverse optimal transport, SIAM J. Appl. Math 80(1), 2020 Arxiv
36. M. Burger, J.F. Pietschmann, M.T. Wolfram, Data assimilation in price formation, Inverse Problems 36(6), 2020 Arxiv
37. J. Carrillo, K. Hopf, M.T. Wolfram, Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons, Kinet. Relat. Math. 13(3), 2020 Arxiv
38. L. Alasio, H. Ranetbauer, M. Schmidtchen, M.T. Wolfram, Trend to equilibrium for systems with small cross diffusion, M2AN 54(5), 2020 Arxiv
39. M. Fischer, G. Jankowiak, M.T. Wolfram, Micro- and macroscopic modeling of crowding and pushing in corridors, NHM 15(3), 2020 Arxiv
40. C. Totzeck, M.T. Wolfram, Consensus-based global optimisation with personal best, Math. Biosci. Eng 17(5)., 2020 Arxiv
41. J. Carrillo, D. Matthes, M.T. Wolfram, Lagrangian schemes for Wasserstein gradient flows, Handbook of Numerical Analysis 22, 2021 Arxiv
42. M. Bruna, M. Burger, J.F. Pietschmann, and M.T. Wolfram, Active Crowds, Active Particles, Volume III, 2021 Arxiv
43. M. Burger, J.-F. Pietschmann, H. Ranetbauer, C. Schmeiser, M.T. Wolfram, Mean field models for segregation dynamics, EJAM 33(1), 2022 Arxiv
44. B. Duering, M. Fischer, M.T. Wolfram, An Elo-type rating model for players and teams of variable strength, Phil Trans R Soc A 380, 2022 Arxiv
45. M. Barker, P. Degond, M.T. Wolfram, Comparing the best reply strategy and mean field games: the stationary case, EJAM 33(1), 2022 Arxiv
46. A. Iuorio, G. Jankowiak, P. Szmolyan, and M.T. Wolfram, A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour, J Math Anal Appl 510(2), 2022 Arxiv
47. O. R. A. Dunbar, A. Duncan, A.M. Stuart, and M.T. Wolfram, Ensemble Inference Methods for Models with Noisy and Expensive Liklihoods, SIADS 21(2), 2022 Arxiv
48. D. Amadori, B. Andreianov, M. Di Francesco, S. Fagiolo, T. Girard, P. Goatin, P. Markowich, J.-F. Pietschmann, M.D. Rosini, G. Russo, G. Stivaletta and M.T. Wolfram, The mathematical theory of Hughes' model: a survery of results, Crowd Dynamics (4), Springer, 2023
49. B. During, J. Evans and M.T. Wolfram, Steady States of an Elo-type Rating Model with Variable Strength, accepted at KRM, 2023 Arxiv
50. A. Iuorio, G. Jankowiak, P. Szmolyan, M.T. Wolfram, Canards in a bottleneck, Physica D 451 2023 Arxiv
51. S. Gomes, A. J. Nugent and M.T. Wolfram, On evolving network models and their influence on opinion formation, Physica D 456 2023 Arxiv
52. M. Burger, L. Kanzler and M.T. Wolfram, Boltzmann mean-field game model for knowledge growth: limits to learning and general utilities, Comm. Math. Sci 22(4), 2024 Arxiv
53. A. Nungent, S. Gomes and M.T. Wolfram, Bridging the gap between agent based models and continuous opinion dynamics, Physica A 651, 2024 Arxiv
54. A. Nungent, S. Gomes and M.T. Wolfram, Steering opinion dynamics through control of social networks, Chaos 34(7), 2024 Arxiv
55. B. During, J. Franceschi, M.T. Wolfram and M. Zanella, Breaking consensus in kinetic opinion formation models on graphons, Journal of Nonlinear Science 34, 2024 Arxiv
56. A. Nugent, S. Homes, M.T. Wolfram, Opinion Dynamics with Continuous Age Structure, accepted at EJAM, 2025 Arxiv
57. T Gaskin, M.T. Wolfram, A. Duncan and G. Demirel, Modelling Global Trade with Optimal Transport, accepted at Nature Communications, 2025 Arxiv
58. H. Bartel, M. Burger and MTW, Multi-Dimensional Opinion Formation, accepted for publication at Proc Royal Soc A 2026 Arxiv
59. S. Glendinning, S. Gomes and M.T. Wolfram, What is the optimal way to lie? From microscopic to kinetic descriptions of consensus control, accepted for publication at the Journal for Nonlinear Science, 2026

Conference proceedings

1. M. Burger, M.T. Wolfram, Inverse dopant profiling for highly doped semiconductor devices,Proceedings of 5th MathMod, Vienna, 2006
2. M.T. Wolfram, Opinion formation in a heterogenuous society, Proceedings of the Econophys V, India, 2010
3. M. Buger, M. Di Francesco, P. Markowich, M.T. Wolfram, On a Mean Field Game Optimal Control Approach Modeling Fast Exit Scenarios in Human Crowds, 52nd IEEE Conference on Decision and Control, 3128--3133, 2013.
4. D. Gomes, R.M. Vehlo, M.T. Wolfram, Dual two state mean field games, 53rd IEEE Conference on Decision and Control, 2014
5. A. Festa, M.T. Wolfram, Collision avoidance in pedestrian dynamics, submitted, accepted at the 54th IEEE Conference on Decision and Control, 2015.
6. C. Koutschan, H. Ranetbauer, G. Regensburger, M.T. Wolfram, Symbolic derivation of Mean-Field PDEs from Lattice Based Models, accepted at the SYNASC, 2015.

Technical Reports

1. M. Bruna, M. Burger, H. Ranetbauer and M.T. Wolfram, Asymptotic gradient flow structures of a nonlinear Fokker-Planck equations, 2017 Arxiv

Preprints

1. G. Estrada-Rodriguez, V. Villegas-Moral, M.T. Wolfram, Decision making in heterogeneous self-propelled particle systems, 2025 Arxiv
2. J. Duddy, S. Gomes and M.T. Wolfram, Analysis of Stationary Solutions for a Nonlinear Pedestrian Flow Model, 2026, submitted