

1987  Diploma in Mathematics, University of Bonn  1989  PhD, HeriotWatt 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 


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 phasetransforming 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 lowhysteresis 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.


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”


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. 


[ 1] Stefan Müller
Homogenization of nonconvex integral functionals and cellular elastic materials Arch. Rational Mech. Anal. , 99: (3): 189212 1987 ISSN: 00039527 DOI: 10.1007/BF00284506[ 2] Robert V. Kohn, Stefan Müller
Surface energy and microstructure in coherent phase transitions Comm. Pure Appl. Math. , 47: (4): 405435 1994 ISSN: 00103640 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): 169204 1993 ISSN: 09442669 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): 779819 2011 ISSN: 00039527 DOI: 10.1007/s0020501003337[ 5] Gero Friesecke, Richard D. James, Stefan Müller
A hierarchy of plate models derived from nonlinear elasticity by gammaconvergence Arch. Ration. Mech. Anal. , 180: (2): 183236 2006 ISSN: 00039527 DOI: 10.1007/s0020500504007[ 6] Gero Friesecke, Richard D. James, Stefan Müller
A theorem on geometric rigidity and the derivation of nonlinear plate theory from threedimensional elasticity Comm. Pure Appl. Math. , 55: (11): 14611506 2002 ISSN: 00103640 DOI: 10.1002/cpa.10048[ 7] Antonio DeSimone, Robert V. Kohn, Stefan Müller, Felix Otto
A reduced theory for thinfilm micromagnetics Comm. Pure Appl. Math. , 55: (11): 14081460 2002 ISSN: 00103640 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: : 43324352 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): 589617 1997 ISSN: 00209910 DOI: 10.1007/s002220050195[ 10] S. Müller, V. Sverák
Convex integration for Lipschitz mappings and counterexamples to regularity Ann. of Math. (2) , 157: (3): 715742 2003 ISSN: 0003486X DOI: 10.4007/annals.2003.157.715



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


1992  Prize of the European Mathematical Society  1993  Max Planck Research Award (jointly with V. Sverák)  1999  Member of the BerlinBrandenburg 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 RhineWestphalian Academy of Sciences, Humanities and the Arts  2015  Member of the Academia Europaea 


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) 


Bernd Kirchheim (2001), now Professor, University of Leipzig
Georg Dolzmann (2002), now Professor, University of Regensburg
Sergio Conti (2004), now Professor, University of Bonn


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


 PhD theses: 14, currently 2


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