Profile
Profile

Prof. Dr. Stefan Müller

Hausdorff Chair / 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

Academic Career

1987

Diploma in Mathematics, University of Bonn

1989

PhD, Heriot-Watt University, Edinburgh, Scotland, UK

1989 - 1990

Visiting Assistant Professor, Carnegie Mellon University, Pittsburgh, PA, USA

1990 - 1993

Postdoc, SFB 256, University of Bonn

1993 - 1994

Visiting Member, Institute of Advanced Study, Princeton, NJ, USA

1994

Professor, University of Freiburg

1995

Professor, ETH Zürich, Switzerland

1996 - 2008

Director, Max Planck Institute for Mathematics in the Sciences, Leipzig

Since 2008

Professor (C4), University of Bonn

Since 2010

External Scientific Member, Max Planck Institute for Mathematics, 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.

Research Projects and Activities

DFG Collaborative Research Centre SFB 1060 “The Mathematics of Emergent Effects”

DFG Research Group 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.

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

Publication List

Editorships

• Archive of Rational Mechanics and Analysis
• Interfaces and Free Boundaries
• Journal of Analysis and its Applications
• M3AS

Awards

1992

Prize of the European Mathematical Society

1993

Max Planck Research Award (jointly with V. Sverák)

1999

Member of the Berlin-Brandenburg Academy of Sciences and Humanities

1999

Collatz Prize of CICIAM

2000

Leibniz Prize

2002

Member of the Leopoldina (German National Academy of Sciences)

2013

Heinz Gumin Prize Mathematics of the Carl Friedrich von Siemens Foundation

2014

Member of the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts

2015

Member of the Academia Europaea

Selected Invited Lectures

1994

Plenary: German Mathematical Society

1996

ECM, Budapest, Hungary

1997

Austrian Mathematical Society

1997

Andrejewski Lectures, Berlin

1998

ICM, Berlin

1998

GAMM, Bremen

1999

ICIAM, Edinburgh, Scotland, UK

2000

Ordway Lectures, Minneapolis, MN, USA

2003

Landau Lectures, Jerusalem, Israel

2006

Gauss Lecture, Bremen

2006

ICMP, Rio de Janeiro, Brasil

2009

Annual Meeting of Leopoldina (German National Academy of Sciences)

Habilitations

Bernd Kirchheim (2001), now Professor, University of Leipzig

Georg Dolzmann (2002), now Professor, University of Regensburg

Sergio Conti (2004), now Professor, University of Bonn

Selected PhD students

Anja Schlömerkemper (2002): “Magnetic Forces in Discrete and Continuous Systems”,
now Professor, University of Würzburg

Christof Melcher (2002): “Néel walls and regularity in thin film micromagnetics”,
now Professor, RWTH Aachen University

László Székelyhidi Jr. (2004): “Elliptic Regularity versus Rank-One Convexity”,
now Professor, University of Leipzig

Bernd Schmidt (2006): “Effective theories for thin elastic films”,
now Professor, University of Augsburg

Supervised Theses

  • PhD theses: 14, currently 2
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