Profile
Profile

Prof. Dr. (em.) Werner Müller

E-mail: mueller(at)math.uni-bonn.de
Phone: +49 228 73 2840
Homepage: http://www.math.uni-bonn.de/people/mueller/
Room: 1.035
Location: Mathematics Center
Institute: Mathematical Institute
Research Areas: Former Research Area D (Leader)
Research Area A
Research Area DE
Research Area G (until 10/2012)
Birthdate: 07.Sep 1947
Mathscinet-Number: 197858

Academic Career

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

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, Cluster of Excellence in 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.
Research Area DE

Selected Publications

[1] Werner Müller, Gorm Salomonsen
Scattering theory for the Laplacian on manifolds with bounded curvature
J. Funct. Anal. , 253: (1): 158--206
2007
ISSN: 0022-1236
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
2010
ISSN: 1016-443X
DOI: 10.1007/s00039-010-0079-2
[4] Werner Müller
Weyl's law for the cuspidal spectrum of {SL_n}
Ann. of Math. (2) , 165: (1): 275--333
2007
ISSN: 0003-486X
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
2009
ISSN: 0012-7094
DOI: 10.1215/00127094-2009-037
[7] Werner Müller
Analytic torsion and R-torsion of Riemannian manifolds
Adv. in Math. , 28: (3): 233--305
1978
ISSN: 0001-8708
DOI: 10.1016/0001-8708(78)90116-0
[8] Werner Müller
Analytic torsion and R-torsion for unimodular representations
J. Amer. Math. Soc. , 6: (3): 721--753
1993
ISSN: 0894-0347
DOI: 10.2307/2152781
[9] Werner Müller
The trace class conjecture in the theory of automorphic forms
Ann. of Math. (2) , 130: (3): 473--529
1989
ISSN: 0003-486X
DOI: 10.2307/1971453
[10] Werner Müller
Relative zeta functions, relative determinants and scattering theory
Comm. Math. Phys. , 192: (2): 309--347
1998
ISSN: 0010-3616
DOI: 10.1007/s002200050301

Publication List

Editorships

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

Awards

1983

Euler-Medal, Academy of Sciences of GDR

1991

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

1993

Member of the Berlin-Brandenburg Academy of Sciences and Humanities

2003

Member of the German National Academy of Sciences Leopoldina

2015

Member of Academia Europaea

Selected Invited Lectures

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

Habilitations

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

Supervised Theses

  • Diplom theses: 12
  • PhD theses: 11, currently 2
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