Prof. Dr. Matthias Erbar
Kurzlebenslauf
seit 2020 | Professor (W3), Fakultät für Mathematik, Universität Bielefeld |
---|---|
seit 2020 | Principal investigator im SFB 1283 Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications |
2020–2023 | Project Ricci Flows for Non-smooth Spaces, Monotonic Quantities, and Rigidity within SPP 2026 Geometry at Infinity |
2020–2023 | Project Optimal Transport for Stationary Point Processes within SPP 2265 Random geometric systems |
2019 | Habilitation in Mathematik, Krümmungsschranken und Gradientenflussstrukturen für interagierende stochastische Teilchensysteme und kinetische Modelle, Universität Bonn |
2017–2020 | Principal investigator im SFB 1060 The Mathematics of Emergent Effects |
2016–2020 | Postdoc (Akademischer Rat a.Z.), Institut für angewandte Mathematik, Universität Bonn |
2014–2016 | Postdoc (Wiss. Ang.), Institut für angewandte Mathematik, Universität Bonn |
2014 | Postdoc, Scuola Normale Superiore, Pisa |
2013 | Postdoc, Mathematical Science Research Institute, Berkeley |
2013 | Promotion, Betreuer Karl-Theodor Sturm, Mathematics, Universität Bonn |
2008–2009 | Studium der Physik, Université Paris VI |
2003–2008 | Studium der Mathematik und Physik, Universität Bonn |
Publikationen
-
2025; SFB 1283 2. Förderphase, TP A08: Variationelle Strukturen für Evolutionsgleichungen, optimaler Transport und synthetische Krümmungsbegriffe; Erbar, Matthias; Deutsche Forschungsgemeinschaft
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2023; Ricci Fluss für singuläre Räume, monotone Funktionale und Starrheit; Erbar, Matthias; Deutsche Forschungsgemeinschaft
- Erbar M. A gradient flow approach to the Boltzmann equation. J. Eur. Math. Soc. (JEMS). 2023.
- Erbar M, Justiniano J, Rumpf M. Approximation of splines in Wasserstein spaces. arXiv:2302.10682. 2023.
- Burger M, Erbar M, Hoffmann F, Matthes D, Schlichting A. Covariance-modulated optimal transport and gradient flows. arXiv:2302.07773. 2023.
- Erbar M, Huesmann M, Jalowy J, M\ B. Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy. arXiv:2304.11145. 2023.
- Erbar M, Forkert D, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media: An Applied Mathematics Journal. 2022;17(5):687-717.
- Erbar M, Rigoni C, Sturm K-T, Tamanini L. Tamed spaces – Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées. 2022;161:1-69.
- Erbar M, Sturm K-T. Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS). 2021;23(1):219-235.
- Erbar M, Huesmann M, Leblé T. The one-dimensional log-gas free energy has a unique minimizer. Comm. Pure Appl. Math. 2021;74(3):615-675.
- Erbar M, Rumpf M, Schmitzer B, Simon S. Computation of optimal transport on discrete metric measure spaces. Numer. Math. 2020;144(1):157-200.
- Erbar M, Fathi M, Schlichting A. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA Lat. Am. J. Probab. Math. Stat. 2020;17(1):445-471.
- Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal transport. Calc. Var. Partial Differential Equations. 2019;58(1):Paper No. 19, 19.
- Erbar M, Fathi M. Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature. J. Funct. Anal. 2018;274(11):3056-3089.
- Erbar M, Juillet N. Smoothing and non-smoothing via a flow tangent to the Ricci flow. J. Math. Pures Appl. (9). 2018;110:123-154.
- Erbar M, Henderson C, Menz G, Tetali P. Ricci curvature bounds for weakly interacting Markov chains. Electron. J. Probab. 2017;22:Paper No. 40, 23.
- Erbar M, Fathi M, Laschos V, Schlichting A. Gradient flow structure for McKean-Vlasov equations on discrete spaces. Discrete Contin. Dyn. Syst. 2016;36(12):6799-6833.
- Ambrosio L, Erbar M, Savar\'{e} G. Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal. 2016;137:77-134.
- Erbar M, Huesmann M. Curvature bounds for configuration spaces. Calc. Var. Partial Differential Equations. 2015;54(1):397-430.
- Erbar M, Maas J, Tetali P. Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models. Ann. Fac. Sci. Toulouse Math. (6). 2015;24(4):781-800.
- Erbar M, Maas J, Renger DRM. From large deviations to Wasserstein gradient flows in multiple dimensions. Electron. Commun. Probab. 2015;20:no. 89, 12.
- Erbar M, Kuwada K, Sturm K-T. On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces. Invent. Math. 2015;201(3):993-1071.
- Erbar M. Gradient flows of the entropy for jump processes. Ann. Inst. Henri Poincaré Probab. Stat. 2014;50(3):920-945.
- Erbar M, Maas J. Gradient flow structures for discrete porous medium equations. Discrete Contin. Dyn. Syst. 2014;34(4):1355-1374.
- Erbar M, Maas J. Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal. 2012;206(3):997-1038.
- Erbar M. The heat equation on manifolds as a gradient flow in the Wasserstein space. Ann. Inst. Henri Poincaré Probab. Stat. 2010;46(1):1-23.
Publikationsliste
Publikationsliste (CSV)
Publikationsliste (PDF) im "AMA"-Zitierstil
Publikationsliste (PDF) im "APA (6th ed.)"-Zitierstil
Publikationsliste (PDF) im "Chicago"-Zitierstil
Publikationsliste (PDF) im "Frontiers"-Zitierstil
Publikationsliste (PDF) im "Harvard"-Zitierstil
Publikationsliste (PDF) im "IEEE"-Zitierstil
Publikationsliste (PDF) im "LNCS"-Zitierstil
Publikationsliste (PDF) im "MLA"-Zitierstil
Download
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Kurzlebenslauf
seit 2020 | Professor (W3), Fakultät für Mathematik, Universität Bielefeld |
---|---|
seit 2020 | Principal investigator im SFB 1283 Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications |
2020–2023 | Project Ricci Flows for Non-smooth Spaces, Monotonic Quantities, and Rigidity within SPP 2026 Geometry at Infinity |
2020–2023 | Project Optimal Transport for Stationary Point Processes within SPP 2265 Random geometric systems |
2019 | Habilitation in Mathematik, Krümmungsschranken und Gradientenflussstrukturen für interagierende stochastische Teilchensysteme und kinetische Modelle, Universität Bonn |
2017–2020 | Principal investigator im SFB 1060 The Mathematics of Emergent Effects |
2016–2020 | Postdoc (Akademischer Rat a.Z.), Institut für angewandte Mathematik, Universität Bonn |
2014–2016 | Postdoc (Wiss. Ang.), Institut für angewandte Mathematik, Universität Bonn |
2014 | Postdoc, Scuola Normale Superiore, Pisa |
2013 | Postdoc, Mathematical Science Research Institute, Berkeley |
2013 | Promotion, Betreuer Karl-Theodor Sturm, Mathematics, Universität Bonn |
2008–2009 | Studium der Physik, Université Paris VI |
2003–2008 | Studium der Mathematik und Physik, Universität Bonn |
Publikationen
-
2025; SFB 1283 2. Förderphase, TP A08: Variationelle Strukturen für Evolutionsgleichungen, optimaler Transport und synthetische Krümmungsbegriffe; Erbar, Matthias; Deutsche Forschungsgemeinschaft
-
2023; Ricci Fluss für singuläre Räume, monotone Funktionale und Starrheit; Erbar, Matthias; Deutsche Forschungsgemeinschaft
- Erbar M. A gradient flow approach to the Boltzmann equation. J. Eur. Math. Soc. (JEMS). 2023.
- Erbar M, Justiniano J, Rumpf M. Approximation of splines in Wasserstein spaces. arXiv:2302.10682. 2023.
- Burger M, Erbar M, Hoffmann F, Matthes D, Schlichting A. Covariance-modulated optimal transport and gradient flows. arXiv:2302.07773. 2023.
- Erbar M, Huesmann M, Jalowy J, M\ B. Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy. arXiv:2304.11145. 2023.
- Erbar M, Forkert D, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media: An Applied Mathematics Journal. 2022;17(5):687-717.
- Erbar M, Rigoni C, Sturm K-T, Tamanini L. Tamed spaces – Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées. 2022;161:1-69.
- Erbar M, Sturm K-T. Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS). 2021;23(1):219-235.
- Erbar M, Huesmann M, Leblé T. The one-dimensional log-gas free energy has a unique minimizer. Comm. Pure Appl. Math. 2021;74(3):615-675.
- Erbar M, Rumpf M, Schmitzer B, Simon S. Computation of optimal transport on discrete metric measure spaces. Numer. Math. 2020;144(1):157-200.
- Erbar M, Fathi M, Schlichting A. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA Lat. Am. J. Probab. Math. Stat. 2020;17(1):445-471.
- Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal transport. Calc. Var. Partial Differential Equations. 2019;58(1):Paper No. 19, 19.
- Erbar M, Fathi M. Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature. J. Funct. Anal. 2018;274(11):3056-3089.
- Erbar M, Juillet N. Smoothing and non-smoothing via a flow tangent to the Ricci flow. J. Math. Pures Appl. (9). 2018;110:123-154.
- Erbar M, Henderson C, Menz G, Tetali P. Ricci curvature bounds for weakly interacting Markov chains. Electron. J. Probab. 2017;22:Paper No. 40, 23.
- Erbar M, Fathi M, Laschos V, Schlichting A. Gradient flow structure for McKean-Vlasov equations on discrete spaces. Discrete Contin. Dyn. Syst. 2016;36(12):6799-6833.
- Ambrosio L, Erbar M, Savar\'{e} G. Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces. Nonlinear Anal. 2016;137:77-134.
- Erbar M, Huesmann M. Curvature bounds for configuration spaces. Calc. Var. Partial Differential Equations. 2015;54(1):397-430.
- Erbar M, Maas J, Tetali P. Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models. Ann. Fac. Sci. Toulouse Math. (6). 2015;24(4):781-800.
- Erbar M, Maas J, Renger DRM. From large deviations to Wasserstein gradient flows in multiple dimensions. Electron. Commun. Probab. 2015;20:no. 89, 12.
- Erbar M, Kuwada K, Sturm K-T. On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces. Invent. Math. 2015;201(3):993-1071.
- Erbar M. Gradient flows of the entropy for jump processes. Ann. Inst. Henri Poincaré Probab. Stat. 2014;50(3):920-945.
- Erbar M, Maas J. Gradient flow structures for discrete porous medium equations. Discrete Contin. Dyn. Syst. 2014;34(4):1355-1374.
- Erbar M, Maas J. Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal. 2012;206(3):997-1038.
- Erbar M. The heat equation on manifolds as a gradient flow in the Wasserstein space. Ann. Inst. Henri Poincaré Probab. Stat. 2010;46(1):1-23.
Publikationsliste
Publikationsliste (CSV)
Publikationsliste (PDF) im "AMA"-Zitierstil
Publikationsliste (PDF) im "APA (6th ed.)"-Zitierstil
Publikationsliste (PDF) im "Chicago"-Zitierstil
Publikationsliste (PDF) im "Frontiers"-Zitierstil
Publikationsliste (PDF) im "Harvard"-Zitierstil
Publikationsliste (PDF) im "IEEE"-Zitierstil
Publikationsliste (PDF) im "LNCS"-Zitierstil
Publikationsliste (PDF) im "MLA"-Zitierstil
Download
RDF/XML-Format
JSON-LD-Format
Turtle-Format
N3-Format