Welcome

I am a post-doc at the Weierstraß Institute for Applied Analysis and Stochastics, Berlin, and member of the research group Partial Differential Equations of Alexander Mielke.

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 MATH+ projects Tr-SE18 Models for heat and charge-carrier flow in organic electronics and AA2-1 Hybrid models for the electrothermal behavior of organic semiconductor devices.

I have been awarded the ISIMM Junior Prize 2018 at STAMM conference "Mathematics & Mechanics: Natural Philosophy in the 21st Century" in Oxford.

Contact
E-mail Matthias.Liero-please remove this text-@wias-berlin.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 Gamma-convergence. In a joint work with U. Stefanelli (Vienna), we extended the Weighted-Energy-Dissipation 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 light-emitting diodes, has become an essential application for me. I work closely with my colleagues Annegret Glitzky, Thomas Koprucki, Jürgen Fuhrmann, and Duy-Hai 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 light-emitting diodes. This was the first model to correctly predict S-shaped current-voltage 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 so-called Hellinger-Kantorovich 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:

Publications

Short CV

1982Born in Berlin, Germany
2002 Abitur, Carl-von-Ossietzky Gymnasium, Berlin
2002 -- 2003Civilian service, Charité Berlin
2003 -- 2008Study of Mathematics (minor in Physics) at Humboldt-Universität zu Berlin, Diploma Thesis: Herleitung eines elastoplastischen Plattenmodells mit Methoden der Γ-Konvergenz (supervisor: Prof. Dr. Alexander Mielke)
2006 -- 2007Student 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 Humboldt-Universität 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 27-29, 2013. For details see the website or the poster (PDF).

Foto

Matthias Liero

Self-heating 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 S-shaped current-voltage 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 Field-Effect 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).