Prof. Dr. (em.) Werner Müller

E-Mail: mueller(at)
Telefon: +49 228 73 2840
Raum: 1.035
Standort: Mathematics Center
Institute: Mathematical Institute
Forschungsbereiche: Former Research Area D (Leader)
Research Area A
Research Area DE
Research Area G (until 10/2012)
Geburtsdatum: 07.Sep 1947
Mathscinet-Number: 197858

Academic Career


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

Research Profile

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.

Research Projects and Activities

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, DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator

Contribution to Research Areas

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 non-compact Riemannian manifolds with special structures at infinity such as manifolds with singularities and locally symmetric spaces of finite volume. In the non-compact 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 Eisenbud-Wigner time delay operator. In [3], I have extended the Selberg trace formula to non-unitary 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 SL(n). 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.

Selected Publications

[1] Werner Müller, Gorm Salomonsen
Scattering theory for the Laplacian on manifolds with bounded curvature
J. Funct. Anal. , 253: (1): 158--206
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): 741--778
DOI: 10.1007/s00039-010-0079-2
[3] Werner Müller
A Selberg trace formula for non-unitary twists
Int. Math. Res. Not. IMRN (9): 2068--2109
DOI: 10.1093/imrn/rnq146
[4] Werner Müller
Weyl's law for the cuspidal spectrum of {SL_n}
Ann. of Math. (2)
, 165: (1): 275--333
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): 117--155
DOI: 10.1215/00127094-2009-037
[6] Tobias Finis, Erez Lapid, Werner Müller
On the spectral side of Arthur's trace formula---absolute convergence
Ann. of Math. (2) , 174: (1): 173--195
DOI: 10.4007/annals.2011.174.1.5
[7] Tobias Finis, Erez Lapid, Werner Müller
Limit multiplicities for principal congruence subgroups of {GL(n)} and {SL(n)}
J. Inst. Math. Jussieu , 14: (3): 589--638
DOI: 10.1017/S1474748014000103
[8] Werner Müller, Jonathan Pfaff
On the growth of torsion in the cohomology of arithmetic groups
Math. Ann. , 359: (1-2): 537--555
DOI: 10.1007/s00208-014-1014-x
[9] Werner Müller, Jonathan Pfaff
Analytic torsion and L2-torsion of compact locally symmetric manifolds
J. Differential Geom. , 95: (1): 71--119
[10] Simon Marshall, Werner Müller
On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds
Duke Math. J. , 162: (5): 863--888
DOI: 10.1215/00127094-2080850
[11] Werner Müller
Analytic torsion and R-torsion for unimodular representations
J. Amer. Math. Soc. , 6: (3): 721--753
DOI: 10.2307/2152781
[12] Werner Müller
The trace class conjecture in the theory of automorphic forms
Ann. of Math. (2) , 130: (3): 473--529
DOI: 10.2307/1971453

Publication List


• Mathematische Nachrichten (1990 - 2005)
• Inventiones Mathematicae (1991 - 2007)
• Compositio Mathematicae (1993 - 1998)
• Intern. Math. Research Notices (1993 - 1998)
• Analysis & PDE (since 2008)



Euler-Medal, Academy of Sciences of GDR


Max Planck Research Award (together with J. Cheeger, Courant Institute)


Member of the Berlin-Brandenburg Academy of Sciences and Humanities


Member of the German National Academy of Sciences Leopoldina


Member of the Academia Europaea

Selected Invited Lectures


ICM, invited speaker, Warsaw, Poland


Taneguichi Symposium, Japan


ECM, invited speaker, Paris, France


Conference in honor of M. Atiyah, R. Bott, F. Hirzebruch, and I. M. Singer, Harvard, MA, USA


Conference in honor of J. Arthur, Toronto, ON, Canada


Clay senior scholar, Lectures at MSRI, Berkeley, CA, USA


Distinguished Ordway Lecturer, University of Minnesota, Minneapolis, MN, USA


Conference in honor of J.-M. Bismut, Paris, France


Conference in honor of J. Schwermer, Max Planck Institute for Mathematics, Bonn


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

Selected PhD students

Werner Hoffmann (1986): “Die Spurformel für Hecke-Operatoren 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 Hodge-Laplaceoperators 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

Jonathan Pfaff (2012): “Selberg and Ruelle zeta functions and the relative analytic torsion
on complete odd-dimensional hyperbolic manifolds of finite volume”

Ksenia Fedosova (2016): “Selber zeta functions and relative analytic torsion for hyperbolic
odd-dimensional orbifolds”

Supervised Theses

  • Master theses: 10
  • Diplom theses: 12
  • PhD theses: 14
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