This page was part of the old http://www.mathematics.uni-bonn.de page, before it was redesigned. We just provide this page, as its contents would have been lost otherwise. Please do not rely on any dates or responsibilites stated on this page, it is not maintained anymore.

* September 7, 1949

Werner Müller

Mathematical Institute

Academic career

1977	PhD, Humboldt Berlin University
1977-1986	Research scholar, Academy of Sciences of GDR
1987-1989	Professor, Academy of Sciences of GDR
1989-1990	Member of the Institute of Advanced Study,
	Princeton, U.S.A.
1990-1993	Member of the Max Planck Institute of
	Mathematics, Bonn
1993-	C4 professor, Bonn University

Awards

1983 Euler-Medal, Academy of Sciences of GDR
1991 Max-Planck-Forschungspreis (together with J. Cheeger, Courant Institute)
1993 Member of Berlin-Brandenburgische Akademie der Wissenschaften
2003 Member of Akademie der Naturforscher Leopoldina, Halle

Offers

Bielefeld University (1992), FU Berlin (1992), Humboldt Berlin University (1995), University of Pennsylvania, Philadelphia, U.S.A. (2005)

Invited lectures

ICM 1983, Taneguichi Symposium (Japan, 1988), ECM 1992, Séminaire Bourbaki (Paris, 1994), Conference in honor of M. Atiyah, R. Bott, F. Hirzebruch and I.M. Singer (Harvard, 1999), Conference in honor of J. Arthur (Toronto, 2004)

Editorship

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

Research projects and activities

DFG Priority Program ``Global Differential Geometry'', Collaborative Research Center SFB 611 ``Singular phenomena and scaling in mathematical models'', GIF Research Grant (together with E. Lapid, Jerusalem)

Research profile

My main interest is in Global Analysis and Automorphic Forms. Global Analysis is the study of differential operators on manifolds. The investigation of solutions of partial differential equations on manifolds is the source of important connections between geometry, topology, and analysis. The study of the spectrum of the Laplace operator on locally symmetric spaces is closely related with the theory of automorphic forms and plays an important rôle in number theory.

Contribution to research area "Geometry of differential operators"

My research in this area is mainly concerned with the study of the spectrum of geometric differential operators on manifolds. In [2,4,9], I studied regularized determinants of elliptic operators which are important in various other fields of mathematics like Arakelov geometry, quantum field theory, inverse spectral theory and topology. In [3] the index of generalized Dirac operators on manifolds with corners has been studied. Current research projects include the development of scattering theory for generalized Laplace operators on manifolds with bounded curvature and the study of analytic torsion of hyperbolic manifolds.

Contribution to research area "Automorphic forms: Global analysis and arithmetic"

The study of the spectrum and the eigenfunctions of the algebra of invariant differential operators on quotients of globally symmetric spaces by arithmetic groups is one of the central problems of the modern theory of automorphic forms. There exist deep connections to number theory. Some of the outstanding problems are: 1) The location of the spectrum (Ramanujan conjectures), 2) Existence and construction of cusp forms (Weyl's law), 3) Principle of functoriality. One of the main tools to study these problems is the Arthur-Selberg trace formula. In [6,8], I have studied some of the basic analytic problems connected with the Arthur trace formula. In [7] the trace formula combined with the heat equation has been used to establish Weyl's law for the cuspidal spectrum of congruence quotients of the general linear group. The main result of [1] implies existence of cusp forms for general groups. Current research projects include further study of the trace formula and the behavior of the discrete spectrum with respect to towers of coverings of the initial manifold (limit multiplicities).

Contribution to research area "Stochastics"

Quantum chaos is the investigation of quantum systems whose underlying classical system is chaotic. One of the main issues is the study of the behavior of the eigenfunctions and spectra in the semiclassical limit. The study of the semiclassical properties of the spectrum of the Laplacian on surfaces of constant negative curvature is related to quantum chaos. There are also close relations to random matrix theory which has found important applications in the understanding of zeros of L-functions. Based on the work in [7,8,1] we will study these problems in higher dimensions which means, in particular, the study of the statistical distribution of the eigenvalues and the eigenstates of the Laplacian on locally symmetric spaces of finite volume.

General research topics for PhD theses

Spectral theory of geometric differential operators
Harmonic analysis on semisimple Lie groups and locally symmetric spaces
Analytic theory of automorphic forms and automorphic L-functions

Recent and planned postgraduate teaching

The Atiyah-Singer index theorem (Summer 2004)
Spectral theory of automorphic forms (Winter 2004)
Representation theory and automorphic forms (Summer 2006)

Supervised theses

Diplom theses: 11, currently 2
PhD theses: 11, currently 4

Selected PhD Students

Werner Hoffmann, 1986, The trace formula for Hecke operators over rank one lattices, now: professor (C3), Bielefeld University
Gorm Salomonsen, 1996, Dirac operators and analysis on open manifolds
Boris Vaillant, 2001, Index- and spectral theory for manifolds with fibred cusps

Habilitations

Kai Köhler, 1999, now: professor (C3), Düsseldorf University

Publications

[1]	LABESSE, J.-P., AND MÜLLER, W. Weak Weyl's law for congruence subgroups. Asian J. Math. 8 (2004), 733-745.
[2]	MÜLLER, W. Analytic torsion and R-torsion for unimodular representations. J. Amer. Math. Soc. 6 (1993), 721-753.
[3]	MÜLLER, W. On the index of Dirac operators on manifolds with corners of codimension two. I. J. Diff. Geometry 44 (1996), 97 - 177.
[4]	MÜLLER, W. Relative zeta functions, relative determinants and scattering theory. Comm. Math. Physics 192 (1998), 309-347.
[5]	MÜLLER, W. The trace class conjecture in the theory of automorphic forms.II. Geom. funct. analysis 8 (1998), 315-355.
[6]	MÜLLER, W. On the spectral side of Arthur's trace formula. Geom. funct. anal. 12 (2002), 669-722.
[7]	MÜLLER, W. Weyl's law for the cuspidal spectrum of ${ m SL}\sb n$ . C. R. Math. Acad. Sci. Paris 338 (2004), 347-352.
[8]	MÜLLER, W., SPEH, B., AND LAPID, E. Absolute convergence of the spectral side of the Arthur trace formula for ${ m GL}\sb n$ . Geom. Funct. Anal. 14 (2004), 58-93.
[9]	MÜLLER, W., AND WENDLAND, K. Extremal Kähler metrics and Ray-Singer analytic torsion. Contemporary Math. 242 (1999), 135-160.

projects

lectures

seminars

phd students

homepage