Prof. Dr. Stefan Müller

Associate Director of HIM

E-mail: stefan.mueller(at)hcm.uni-bonn.de
Phone: +49 228 73 62289
Homepage: http://www.hcm.uni-bonn.de/homepages/prof-dr-stefan-mueller/
Room: 2.032
Location: Mathematics Center
Institute: Institute for Applied Mathematics
Max-Planck-Institute for Mathematics
Research Areas: Research Area B (Leader)
Research Area G
Mathscinet-Number: 663408

Publications

Academic Career

1989

PhD, Heriot-Watt University, Edinburgh

1989--1990

Visiting Ass. Prof., Carnegie Mellon University

1990--1993

Postdoc, SFB 256, Bonn University

1993--1994

Visiting Member, IAS Princeton

1994

Full Professor, Freiburg University

1995

Full Professor, ETH Zürich

1996--2008

Director, MPI Mathematics in the Sciences, Leipzig

2008--

Full Professor (C4), Bonn

1987

Diploma in Mathematics, Bonn

2010--

External scientific member, MPI Bonn

Research profile

My goal is to develop mathematical methods to describe and understand multiscale problems and the formation, evolution and macroscopic effects of microstructure, in particular in advanced materials. I have always been fascinated by the subtle interplay of geometry, analysis, and physics in nonlinear elasticity, both for conventional and for phase-transforming materials. Results include a qualitatively new homogenization formula in nonlinear elastic materials [1], the first rigorous understanding of dimension reduction in nonlinear elasticity [5,6] and rigorous scaling laws for branching near austenite/martensite interfaces [2]. Implications for material design, e.g, for low-hysteresis shape memory alloys are explored in [8]. In turn estimates and constructions first discovered in elasticity led to new results in geometry [9] and rather striking counterexamples to Hilbert's 19th problem in PDE [10]. Other important areas are micromagnetics, where a simple, yet subtle, energy functional describes a huge variety of magnetization patterns on very different scales [7] and plasticity [4]. Recently
I have begun work on understanding the relation between atomistic and continuum theory of solids through statistical mechanics and rigorous renormalization.

Selected Publications

[1] Stefan Müller
Homogenization of nonconvex integral functionals and cellular elastic materials
Arch. Rational Mech. Anal. , 99: (3): 189--212
1987
ISSN: 0003-9527
DOI: 10.1007/BF00284506
[2] Robert V. Kohn, Stefan Müller
Surface energy and microstructure in coherent phase transitions
Comm. Pure Appl. Math. , 47: (4): 405--435
1994
ISSN: 0010-3640
DOI: 10.1002/cpa.3160470402
[3] Stefan Müller
Singular perturbations as a selection criterion for periodic minimizing sequences
Calc. Var. Partial Differential Equations , 1: (2): 169--204
1993
ISSN: 0944-2669
DOI: 10.1007/BF01191616
[4] Sergio Conti, Adriana Garroni, Stefan Müller
Singular kernels, multiscale decomposition of microstructure, and dislocation models
Arch. Ration. Mech. Anal. , 199: (3): 779--819
2011
ISSN: 0003-9527
DOI: 10.1007/s00205-010-0333-7
[5] Gero Friesecke, Richard D. James, Stefan Müller
A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
Arch. Ration. Mech. Anal. , 180: (2): 183--236
2006
ISSN: 0003-9527
DOI: 10.1007/s00205-005-0400-7
[6] Gero Friesecke, Richard D. James, Stefan Müller
A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
Comm. Pure Appl. Math. , 55: (11): 1461--1506
2002
ISSN: 0010-3640
DOI: 10.1002/cpa.10048
[7] Antonio DeSimone, Robert V. Kohn, Stefan Müller, Felix Otto
A reduced theory for thin-film micromagnetics
Comm. Pure Appl. Math. , 55: (11): 1408--1460
2002
ISSN: 0010-3640
DOI: 10.1002/cpa.3028
[8] Z.~Y.~Zhang , R.~D.~James , S.~Müller
Energy barriers and hysteresis in martensitic phase transformations
Acta Materialia , 57: : 4332--4352
2009
[9] Alexandre Freire, Stefan Müller, Michael Struwe
Weak convergence of wave maps from (1+2)-dimensional Minkowski space to Riemannian manifolds
Invent. Math. , 130: (3): 589--617
1997
ISSN: 0020-9910
DOI: 10.1007/s002220050195
[10] S. Müller, V. Sverák
Convex integration for Lipschitz mappings and counterexamples to regularity
Ann. of Math. (2) , 157: (3): 715--742
2003
ISSN: 0003-486X
DOI: 10.4007/annals.2003.157.715

Awards

1992

Prize of the European Mathematical Society

1993

Max-Planck Research Prize (jointly with V. Sverák)

1999

Member of the Academy of Berlin-Brandenburg

1999

Collatz prize of CICIAM

2000

Leibniz prize

2002

Member of the Academy Leopoldina

2013

Heinz Gumin Prize Mathematics of the Carl Friedrich von Siemens Foundation

Invited Lectures

1998

ICM, Berlin

2006

ICMP, Rio de Janeiro

1994

Plenary: German Math. Soc.

1996

ECM

1997

Austrian Math. Soc.

1998

GAMM

1999

ICIAM

2009

Annual Meeting of Leopoldina

1997

Andrejewski Lectures Berlin

2000

Ordway Lectures Minneapolis

2003

Landau Lectures Jerusalem

2006

Gauss Lecture Bremen

Editorships

Archive of Rational Mechanics and Analysis; Interfaces and Free Boundaries; Journal of the
European Mathematical Society; Bulletin, Journal and Proceedings of London Mathematical
Society; Journal of Analysis and its Applications;M3 AS.

Research Projects and Activities

DFG SPP 1239: Magnetic Shape Memory; DFG FOR 718: Analysis and Stochastics in Complex
Physical Systems; DFG FOR 797: Microplast – Analysis and computation of microstructure
in finite plasticity.

Contribution to Research Areas

Research Area B
Expertise in nonconvex problems in the calculus of variations and their applications to material microstructure, including recent extensions to atomistic models as well as in a broad range of rigorous multiscale methods, including homogenization [1], singular perturbations [2,3] and <br>Gamma-convergence [4,5,6,7].
Research Area G
Statistical mechanics of solids and thermodynamic limits through rigorous renormalization group methods. Relations between variational methods and small noise limits through capacity estimates and the theory of large deviations.

Habilitations

B. Kirchheim (2001), now Professor Oxford; G. Dolzmann (2002), now Professor Regensburg;
S. Conti (2004), now Professor Bonn.

Selected PhD students

Anja Schlömerkemper (2002), now Professor Würzburg; Christof Melcher (2002), now Professor
Aachen; László Székelyhidi (2004), now Professor Leipzig; Bernd Schmidt (2006), now
Professor Augsburg.

Supervised Theses

  • PhD theses: 14, currently 1
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