Welcome
I am a postdoc at the Weierstraß Institute for Applied Analysis and Stochastics, Berlin, and member of the research group Partial Differential Equations of Alexander Mielke.
I am the scientific employee representative in the executive board of the Einstein Center for Mathematics (ECMath). Together with Carsten Gräser (FU Berlin), Carlos Rautenberg (HU Berlin), and Guillaume Sagnol (TU Berlin) I am organizing the biannual ECMath Colloquium.
I am also a member of the Berlin Mathematical School (BMS) in the Postdoctoral Faculty.
Together with Annegret Glitzky I am head of the Matheon project SE18 Models for heat and chargecarrier flow in organic electronics.
I have been awarded the ISIMM Junior Prize 2018 at STAMM conference "Mathematics & Mechanics: Natural Philosophy in the 21st Century" in Oxford.
ContactMatthias.Liero@wiasberlin.de (Public Key)  
Phone  +49 (0) 30 20372 542 
Fax  +49 (0) 30 20372 311 
Teaching
In the summer term SS2018 I am giving a lecture on Mehrdimensionale Variationsrechnung at Humboldt Universität zu Berlin, Tuesdays from 1pm and Thursdays from 9am. The tutorial is on Tuesday from 3pm.
In the winter term WS2017/18 I was giving a lecture on Optimal transport and Wasserstein gradient flows at Humboldt Universität zu Berlin, Tuesdays from 9am.
Research interests
My mathematical expertise is in the field of nonlinear partial differential equations. In particular, the rigorous derivation of new effective models in various problems in natural sciences using novel mathematical techniques is one of my major interests. In my diploma I gave a rigorous justification of an evolutionary elastoplastic plate model for continuum mechanics using the notion of Gammaconvergence. In a joint work with U. Stefanelli (Vienna), we extended the WeightedEnergyDissipation principle from parabolic to hyperbolic equations to make them accessible to variational methods.
In the recent years, the mathematical modeling, analysis, and simulation of optoelectronic devices, such as solar cells and organic lightemitting diodes, has become an essential application for me. I work closely with my colleagues Annegret Glitzky, Thomas Koprucki, Jürgen Fuhrmann, and DuyHai Doan from WIAS on organic devices. In a joint work with the Dresden Integrated Center for Applied Physics and Photonic Materials, in particular with Axel Fischer, Reinhard Scholz and Sebastian Reineke, we derived a novel PDE model, involving the p(x)Laplacian with discontinuous p(x), to describe the current and heat flow in organic lightemitting diodes. This was the first model to correctly predict Sshaped currentvoltage characteristics with regions of negative differential resistance as observed in measurements.
Moreover, with Michael Sawatzki and Hans Kleemann from IAPP we investigate the behavior and new concepts of organic transistors.
However, also the more abstract theory behind partial differential equations is in the focus of my current work. One particular highlight of a recent joint work with Alexander Mielke (WIAS Berlin) and Giuseppe Savaré (Pavia) was the derivation and characterization of the socalled HellingerKantorovich distance, which can be seen as a generalization of the famous Wasserstein distance to arbitrary measures.
In general, my scientific work is guided by the aim to strengthen the cooperation between analysis and its applications by inventing and further developing the mathematical foundations and techniques to make them applicable for practical questions in other sciences.
Projects
I have been involved in the following projects: MATHEON project SE18 (2017—2018): Models for heat and chargecarrier flow in organic electronics
 MATHEON project SE2 (2014—2017): Electrothermal modeling of largearea OLEDs.
 MATHEON project D22 (2010—2014): Modeling of Electronic Properties of Interfaces in Solar Cells
Publications

F. M. Sawatzki, D. H. Doan, H. Kleemann, M. Liero, A. Glitzky,
Th. Koprucki, K. Leo
Balance of horizontal and vertical charge transport in organic fieldeffect transistors,
Phys. Rev. Applied, 10:034069, 2018. 
A. Glitzky, M. Liero
Instationary driftdiffusion problems with GaussFermi statistics and fielddependent mobility for organic semiconductor devices,
WIAS Preprint 2523 (2018) 
H. D. Doan, A. Glitzky, M. Liero
Driftdiffusion modeling, analysis and simulation of organic semiconductor devices,
WIAS Preprint 2493 (2018)  A. Fischer, M. Pfalz, K. Vandewal, M. Liero, A. Glitzky, S. Lenk, S. Reineke
Full electrothermal OLED model including nonlinear selfheating effects, In: Phys. Rev. Applied, 10:014023, 2018  Doan, DuyHai, Glitzky, Annegret, Liero, Matthias
Driftdiffusion modeling, analysis and simulation of organic semiconductor devices 
Liero, Matthias; Fuhrmann, Jürgen; Glitzky, Annegret; Koprucki, Thomas; Fischer, Axel; Reineke, Sebastian
3D electrothermal simulations of organic LEDs showing negative differential resistance
Appeared In: Opt. Quant. Electron. (2017) 49: 330. https://doi.org/10.1007/s1108201711674 
Liero, Matthias; Melchionna, Stefano
The weighted energydissipation principle and evolutionary Γconvergence for doubly nonlinear problems
To appear in ESAIM: Control, Optimisation and Calculus of Variations 
Fuhrmann, Jürgen; Glitzky, Annegret; Liero, Matthias
Hybrid finitevolume/finiteelement schemes for $p(x)$Laplace thermistor models
Appeared In: Finite Volumes for Complex Applications VIII  Hyperbolic, Elliptic and Parabolic Problems  FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., Springer International Publishing, Cham et al., 2017, pp. 397405.  Bulíček, Miroslav; Glitzky, Annegret; Liero, Matthias
Thermistor systems of p(x)Laplacetype with discontinuous exponents via entropy solutions
Appeared in: SIAM J. Math. Anal., 48 (2016) pp. 34963514.  Disser, Karoline; Liero, Matthias; Zinsl, Jonathan
On the evolutionary Gammaconvergence of gradient systems modeling slow and fast chemical reactions
To appear in Nonlinearity  Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
Optimal entropytransport problems and a new HellingerKantorovich distance between positive measures
Appeared in: Inventiones Mathematicae, 2017, https://doi.org/10.1007/s0022201707598  Bercegol, Adrien and Chacko, Binoy and Klenk, Reiner and Lauermann, Iver and LuxSteiner, Martha Ch. and Liero, Matthias
Point contacts at the copperindiumgalliumselenide interface  A theoretical outlook
Appeared in: Journal of Applied Physics, 119, 155304 (2016).  Bulíček, Miroslav; Glitzky, Annegret; Liero, Matthias
Systems describing electrothermal effects with p(x)Laplacian like structure for discontinuous variable exponents
Appeared In: SIAM J. Math. Anal., 48 (2016) pp. 34963514.  Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
Optimal transport in competition with reaction: The HellingerKantorovich distance and geodesic curves
Appeared In: SIAM J. Math. Anal., 48 (2016) pp. 28692911.  Liero, Matthias; Mielke, Alexander; Peletier, Mark A.; Renger, D. R. Michiel
On microscopic origins of generalized gradient structures
Appeared In: Discrete Contin. Dyn. Syst. Ser. S, 10 (2017) pp. 135.  Glitzky, Annegret; Liero, Matthias
Analysis of p(x)Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices
Appeared In: Nonlinear Anal. Real World Appl., 34 (2017) pp. 536562.  Liero, Matthias; Reichelt, Sina
Homogenization of CahnHilliardtype equations via evolutionary Gammaconvergence
To appear in Nonlinear Differential Equations and Applications NoDEA  Liero, Matthias; Koprucki, Thomas; Fischer, Axel; Scholz, Reinhard; Glitzky, Annegret
pLaplace thermistor modeling of electrothermal feedback in organic semiconductors
Appeared in: ZAMP Z. Angew. Math. Phys., 66 (2015) pp. 29572977.  Disser, Karoline; Liero, Matthias
On gradient structures for Markov chains and the passage to Wasserstein gradient flows
Appeared in: Netw. Heterog. Media, 10 (2015) pp. 233253.  Liero, Matthias; Mielke, Alexander
Gradient structures and geodesic convexity for reactiondiffusion systems
Appeared in: Phil. Trans. R. Soc. A, 371 (2013) pp. 20120346/120120346/28.  Liero, Matthias
Passing from bulk to bulk/surface evolution in the AllenCahn equation
Appeared in: NoDEA Nonlinear Differential Equations Appl., 20 (2013) pp. 919942.  Liero, Matthias; Stefanelli, Ulisse
The ellipticregularization principle in Lagrangian mechanics
Appeared in: J. Nonlinear Sci., 23 (2013) pp. 179204, under the title ``A new minimum principle for Lagrangian mechanics''  Liero, Matthias; Roche, Thomas
Rigorous derivation of a plate theory in linear elastoplasticity via Gamma convergence
Appeared in: NoDEA Nonlinear Differential Equations Appl., 19 (2012) pp. 437457.  Liero, Matthias; Mielke, Alexander
An evolutionary elastoplastic plate model derived via Gamma convergence
Appeared in: Math. Models Methods Appl. Sci., 21 (2011) pp. 19611986.  Krejčí, Pavel; Liero, Matthias
Rate independent Kurzweil processes
Appeared in: Appl. Math., 54 (2009) pp. 117145.  Liero, Matthias and Stefanelli, Ulisse
Weighted InertiaDissipationEnergy functionals for semilinear equations.
Appeared in: Boll. Unione Mat. Ital. (9) 6, 127, 2013.  Liero, Hannelore and Liero, Matthias
Testing the influence function in accelerated life time models.
Appeared In: Statistical models and methods for biomedical and technical systems Eds. F. Vonta, M. Nikulin, N. Limnios and C. Huber, 2008.
Short CV
1982  Born in Berlin, Germany 
2002  Abitur, CarlvonOssietzky Gymnasium, Berlin 
2002  2003  Civilian service, Charité Berlin 
2003  2008  Study of Mathematics (minor in Physics) at HumboldtUniversität zu Berlin, Diploma Thesis: Herleitung eines elastoplastischen Plattenmodells mit Methoden der ΓKonvergenz (supervisor: Prof. Dr. Alexander Mielke) 
2006  2007  Student assistant at WIAS Berlin, Research Group Thermodynamic Modeling and Analysis of Phase Transitions 
2008  2010  PhD student in DFG Research Training Group 1128 Analysis, Numerics, and Optimization of Multiphase Problems 
Feb 2010  Jul 2010  Research period at I.M.A.T.I. Pavia, funded by BioSMA research programme (supervisor: Prof. Dr. Ulisse Stefanelli) 
Aug 2010  Dec 2012  PhD student at WIAS Berlin, MATHEON project D22: Modeling of Electronic Properties of Interfaces in Solar Cells 
Dec 2012  Defense of PhD thesis at HumboldtUniversität zu Berlin: Variational Methods in Evolution (Supervisors: Prof. Dr. Alexander Mielke, Prof. Dr. Ulisse Stefanelli) 
Miscellaneous
Together with Maciek Korzec from TU Berlin I organized a BMS Intensive Course on Evolution Equations and their Applications from November 2729, 2013. For details see the website or the poster (PDF).
 Local organizer of Workshop Mathematics for Semiconductor Heterostructures, September 2012
 Organizer of Workshop Applied Mathematics and Simulation for Semiconductors, March 2015
Selfheating in 2.54mm x 2.54mm OLED sample on glass substrate. The interplay between temperature activated hopping transport and Joule heating leads to complicated electrothermal feedback, leading to Sshaped currentvoltage characteristics with rewgions of negative differential resistance. This behavior was studied in Matheon project SE2 in cooperation with the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP).
Hole density, hole current density and electrostatic potential in Vertical Organic FieldEffect Transistor for applied drain voltage and opening of gate. This behavior was studied in Matheon project SE18 in cooperation with the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP).