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| 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 |
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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.
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[ 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 |
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| 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 |
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| 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 |
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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.
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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.
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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  -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. |
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B. Kirchheim (2001), now Professor Oxford; G. Dolzmann (2002), now Professor Regensburg;
S. Conti (2004), now Professor Bonn.
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Anja Schlömerkemper (2002), now Professor Würzburg; Christof Melcher (2002), now Professor
Aachen; László Székelyhidi (2004), now Professor Leipzig; Bernd Schmidt (2006), now
Professor Augsburg.
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- PhD theses: 14, currently 1
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