

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 main interest is in global analysis and the theory of automorphic forms. Global analysis is concerned with the study of geometric 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 the theory of automorphic forms. The ArthurSelberg trace formula is one of the most important tools in the theory of automorphic forms.
In joint work with T. Finis and E. Lapid I have used the trace formula to study the asymptotic distribution of automorphic forms for . This includes the Weyl law and the limit multiplicity problem. A crucial input is the refined spectral side of the trace formula, which was established in joint work with T. Finis and E. Lapid. A very challenging problem is to extend these results to other classical groups. Among other things, this requires detailed knowledge of the analytic properties of the functions occurring on the spectral side of the trace formula. To this end one can use Arthur's work on the endoscopic classification of automorphic representations of symplectic and orthogonal groups to relate the functions to functions for .
Another key topic of my research in recent years has been the study of analytic torsion of compact locally symmetric manifolds. Analytic torsion is a sophisticated spectral invariant of a compact Riemannian manifold and a flat bundle over this manifold. A basic problem is the approximation of torsion by the analytic torsion of finite coverings in a tower. This is a special case of the kind of problems studied to a great extent by W. Lück. Bergeron and Venkatesh used this to study the torsion in the cohomology of cocompact arithmetic groups if the level is increased. J. Pfaff and I studied the same problem if the arithmetic group is fixed and the local system varies.
Many arithmetic groups are not cocompact and the longterm goal is to extend these results to the finite volume case. The main tool is again the trace formula. Its application leads to problems related to the refined spectral side and the study of weighted orbital integrals, which appear on the geometric side of the trace formula.


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


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.  Research Area DE
In joint work with T. Finis and E. Lapid [4], we settled the limit multiplicity problem for the groups and . In [5] I studied with S. Marshall the growth of the torsion subgroup in the cohomology of a compact arithmetic hyperbolic 3manifold. With J. Pfaff [6] we extended this partially to other compact arithmetic locally symmetric manifolds. With J. Matz we have introduced the analytic torsion for congruence quotients of and studied the approximation of the torsion. 


[ 1] Werner Müller, Gorm Salomonsen
Scattering theory for the Laplacian on manifolds with bounded curvature J. Funct. Anal. , 253: (1): 158206 2007 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 DOI: 10.1007/s0003901000792[ 3] Werner Müller
A Selberg trace formula for nonunitary twists Int. Math. Res. Not. IMRN (9): 20682109 2011 DOI: 10.1093/imrn/rnq146[4] Tobias Finis, Erez Lapid, Werner Müller
Limit multiplicities for principal congruence subgroups of {GL(n)} and {SL(n)} J. Inst. Math. Jussieu , 14: (3): 589638 2015 DOI: 10.1017/S1474748014000103 [ 5] Simon Marshall, Werner Müller
On the torsion in the cohomology of arithmetic hyperbolic 3manifolds Duke Math. J. , 162: (5): 863888 2013 DOI: 10.1215/001270942080850[ 6] Werner Müller, Jonathan Pfaff
On the growth of torsion in the cohomology of arithmetic groups Math. Ann. , 359: (12): 537555 2014 DOI: 10.1007/s002080141014x[ 7] Werner Müller, Jonathan Pfaff
Analytic torsion and L^{2}torsion of compact locally symmetric manifolds J. Differential Geom. , 95: (1): 71119 2013[ 8] Tobias Finis, Erez Lapid, Werner Müller
On the spectral side of Arthur's trace formulaabsolute convergence Ann. of Math. (2) , 174: (1): 173195 2011 DOI: 10.4007/annals.2011.174.1.5[ 9] Erez Lapid, Werner Müller
Spectral asymptotics for arithmetic quotients of {SL(n,\Bbb R)/SO(n)} Duke Math. J. , 149: (1): 117155 2009 DOI: 10.1215/001270942009037[ 10] Werner Müller
Weyl's law for the cuspidal spectrum of {SL_n} Ann. of Math. (2) , 165: (1): 275333 2007 DOI: 10.4007/annals.2007.165.275[ 11] Werner Müller
Analytic torsion and Rtorsion for unimodular representations J. Amer. Math. Soc. , 6: (3): 721753 1993 DOI: 10.2307/2152781[ 12] Werner Müller
The trace class conjecture in the theory of automorphic forms Ann. of Math. (2) , 130: (3): 473529 1989 DOI: 10.2307/1971453[ 14] Werner Müller Jasmin Matz
Analytic torsion of arithmetic quotients of the symmetric space \mathrmSL(n,\mathbbR)/\mathrmSO(n) arXiv: 1607:04676, to appear in GAFA 2016[15] Werner Müller Jasmin Matz
Approximation of L^{2analytic torsion for arithmetic quotients ofthe symmetric space }\mathrmSL(n,\mathbbR)/\mathrmSO(n) arXiv: 1709:07764 2017





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


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 the 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  2013  Conference in honor of J.M. Bismut, Paris, France  2016  Conference in honor of J. Schwermer, Max Planck Institute for Mathematics, Bonn 


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
Jonathan Pfaff (2012): “Selberg and Ruelle zeta functions and the relative analytic torsion
on complete odddimensional hyperbolic manifolds of finite volume”
Ksenia Fedosova (2016): “Selber zeta functions and relative analytic torsion for hyperbolic
odddimensional orbifolds”,
now Research Assistant, University of Freiburg


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


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