

1977  PhD, HU Berlin  1977  1986  Research Scholar, Academy of Sciences of GDR, Berlin  1987  1989  Professor, Academy of Sciences of GDR, Berlin  1989  1990  Member, Institute of Advanced Study, Princeton, NJ, USA  1990  1993  Member, Max Planck Institute for Mathematics, Bonn  1993  2016  Professor (C4), University of Bonn  Since 2016  Professor Emeritus 


My primary interest is in Global Analysis and the theory of automorphic forms. Global Analysis is the study of differential operators on manifolds. The investigation of solutions of partial differential equations of geometric origin is the source of important connections between geometry, topology and analysis. I am especially interested in harmonic analysis on locally symmetric spaces and reductive Lie groups. This is closely related to the theory of automorphic forms.


DFG Priority Programme SPP 1154 “Global Differential Geometry”
Project leader
DFG Collaborative Research Center SFB 611 “Singular phenomena and scaling in mathematical models”
Project leader
GIF Research Project “Analytic aspects of automorphic forms and the trace formula”
Project leader, 2004  2008
GIF Research Project “Spectral methods in automorphic forms”
Project leader, 2008  2011
Research Areas A and D, Cluster of Excellence in Mathematics
Principal Investigator


Research Area A The focus of my research in this area is on the study of the spectrum of geometric differential operators on manifolds and the relation to geometry. Of particular interest are classes of noncompact Riemannian manifolds with special structures at infinity such as manifolds with singularities and locally symmetric spaces of finite volume. In the noncompact case it is important to determine the structure of the continuous spectrum. The main tool is scattering theory.
In [1], we developed scattering theory for Laplace operators on manifolds of bounded curvature. In [2], we have studied scattering theory for differential forms on manifolds with cylindrical ends.
In particular, we have given a cohomological interpretation of the EisenbudWigner time delay operator. In [3], I have extended the Selberg trace formula to nonunitary representations of the fundamental group. This has applications to dynamical zeta functions.  Former Research Area D The modern theory of automorphic forms sets up a deep connection between harmonic analysis on reductive groups over local and global fields and number theory. One of the central problems on the analytic side is to study of the spectrum and the eigenfunctions of the algebra of invariant differential operators on quotients of globally symmetric spaces by arithmetic groups. Some of the basic problems are: (1) determine the location and distribution of the spectrum (Ramanujan conjectures), (2) existence and construction of cusp forms, (3) the principal of functoriality. In [4], I have established Weyl's law for cusp forms on . In a joint paper with E. Lapid [5], we have refined this result in the sense that we consider the spectrum of the full algebra of invariant differential operators and estimate the remainder term. The Arthur trace formula is one of the basic tools in the theory of automorphic forms. In a joint paper with T. Finis and E. Lapid [6], we derived a refinement of the spectral expansion of Arthur's trace formula. The expression is absolutely convergent with respect to the trace norm, which is important for applications.  Research Area DE



[ 1] Werner Müller, Gorm Salomonsen
Scattering theory for the Laplacian on manifolds with bounded curvature J. Funct. Anal. , 253: (1): 158206 2007 ISSN: 00221236 DOI: 10.1016/j.jfa.2007.06.001[ 2] Werner Müller, Alexander Strohmaier
Scattering at low energies on manifolds with cylindrical ends and stable systoles Geom. Funct. Anal. , 20: (3): 741778 2010 ISSN: 1016443X DOI: 10.1007/s0003901000792[ 4] Werner Müller
Weyl's law for the cuspidal spectrum of {SL_n} Ann. of Math. (2) , 165: (1): 275333 2007 ISSN: 0003486X DOI: 10.4007/annals.2007.165.275[ 5] Erez Lapid, Werner Müller
Spectral asymptotics for arithmetic quotients of {SL(n,\Bbb R)/SO(n)} Duke Math. J. , 149: (1): 117155 2009 ISSN: 00127094 DOI: 10.1215/001270942009037[ 7] Werner Müller
Analytic torsion and Rtorsion of Riemannian manifolds Adv. in Math. , 28: (3): 233305 1978 ISSN: 00018708 DOI: 10.1016/00018708(78)901160[ 8] Werner Müller
Analytic torsion and Rtorsion for unimodular representations J. Amer. Math. Soc. , 6: (3): 721753 1993 ISSN: 08940347 DOI: 10.2307/2152781[ 9] Werner Müller
The trace class conjecture in the theory of automorphic forms Ann. of Math. (2) , 130: (3): 473529 1989 ISSN: 0003486X DOI: 10.2307/1971453[ 10] Werner Müller
Relative zeta functions, relative determinants and scattering theory Comm. Math. Phys. , 192: (2): 309347 1998 ISSN: 00103616 DOI: 10.1007/s002200050301



• Mathematische Nachrichten (1990  2005)
• Inventiones Mathematicae (1991  2007)
• Compositio Mathematicae (1993  1998)
• Intern. Math. Research Notices (1993  1998)


1983  EulerMedal, Academy of Sciences of GDR  1991  Max Planck Research Award (together with J. Cheeger, Courant Institute)  1993  Member of the BerlinBrandenburg Academy of Sciences and Humanities  2003  Member of the German National Academy of Sciences Leopoldina  2015  Member of Academia Europaea 


1983  ICM, invited speaker, Warsaw, Poland  1988  Taneguichi Symposium, Japan  1992  ECM, invited speaker, Paris, France  1999  Conference in honor of M. Atiyah, R. Bott, F. Hirzebruch, and I. M. Singer, Harvard, MA, USA  2004  Conference in honor of J. Arthur, Toronto, ON, Canada  2008  Clay senior scholar, Lectures at MSRI, Berkeley, CA, USA  2009  Distinguished Ordway Lecturer, University of Minnesota, Minneapolis, MN, USA 


Kai Köhler (1999), now Professor (C3), University of Düsseldorf


Werner Hoffmann (1986): “Die Spurformel für HeckeOperatoren über Gittern vom Rang”,
now Professor, University of Bielefeld
Gorm Salomonsen (1996): “Dirac operators and analysis on open manifolds”
Boris Vaillant (2001): “Index and Spectral Theory for Manifolds with Fibred Cusps”
Jörn Müller (2008): “Zur Kohomologie und Spektraltheorie des HodgeLaplaceoperators von Mannigfaltigkeiten mit gefaserter Spitzenmetrik”,
now Research Assistant , HU Berlin
Clara Aldana (2009): “Inverse Spectral Theory And Relative Determinants Of Elliptic Operators On Surfaces With Cusps”,
now Postdoctoral Researcher, Mathematics Research Unit, University of Luxembourg, Luxembourg


 Diplom theses: 12
 PhD theses: 11, currently 2


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