Prof. Dr. Matthias Lesch

E-Mail: ml(at)
Telefon: +49 228 73 7641
Raum: 1.033
Standort: Mathematics Center
Institute: Mathematical Institute
Forschungsbereiche: Research Area B3
Interdisciplinary Research Unit D2

Academic Career


Dr. rer. nat., University of Marburg (advisor: Manfred Breuer)

1989 - 1995

Assistant Professor (C1, later C2), University of Augsburg


Habilitation, University of Augsburg

1994 - 1995

Visiting Assistant Professor, The Ohio State University, Columbus, OH, USA (on leave from Augsburg)

1995 - 1999

Senior Assistant Professor (C2), HU Berlin


Heisenberg Fellow, University of Bonn

1999 - 2000

Associate Professor, University of Arizona, Tucson, AZ, USA

2001 - 2005

Professor (C3), University of Cologne

2005 - 2007

Professor (C3), University of Bonn

Since 2007

Professor (W2), University of Bonn

Research Profile

A large part of my research focuses around geometric differential operators (Dirac and Laplace operators) and their spectral theory. In particular I am interested in spectral invariants which may be extracted from the heat kernel (torsion, eta invariants, zeta-determinants, rho invariants).
I am also interested in Noncommutative Geometry a la Connes and I am working on heat invariants in the noncommutative setting. The noncommuative setting exhibits interesting phenomena which are generally not present in the commutative context.

In collaboration with Boris Vertman I have established a work programme on ''spectral geometry, index theory and geometric flows'' in the context singular spaces. One of the main objectives is to establish a heat resp. resolvent expansion for certain Laplace type operators on certain stratified spaces. This would have interesting applications for the understanding of various of the above mentioned spetral invariants.
A second long term project is in operator algebras: I am working on functional analytic problems related to the construction of the celebrated Kasparov product in the unbounded picture of KK-theory.

Selected Publications

[1] Luiz Hartmann, Matthias Lesch, Boris Vertman
Zeta-determinants of Sturm-Liouville operators with quadratic potentials at infinity
J. Differential Equations , 262: (5): 3431--3465
DOI: 10.1016/j.jde.2016.11.033
[2] Matthias Lesch, Henri Moscovici
Modular curvature and Morita equivalence
Geom. Funct. Anal. , 26: (3): 818--873
DOI: 10.1007/s00039-016-0375-6
[3] Matthias Lesch
Divided differences in noncommutative geometry: rearrangement lemma, functional calculus and expansional formula
J. Noncommut. Geom. , 11: (1): 193--223
DOI: 10.4171/JNCG/11-1-6
[4] Alexander Gorokhovsky, Matthias Lesch
On the spectral flow for Dirac operators with local boundary conditions
Int. Math. Res. Not. IMRN (17): 8036--8051
DOI: 10.1093/imrn/rnu188
[5] Matthias Lesch, Boris Vertman
Regularizing infinite sums of zeta-determinants
Math. Ann.
, 361: (3-4): 835--862
DOI: 10.1007/s00208-014-1078-7
[6] Matthias Lesch
A gluing formula for the analytic torsion on singular spaces
Anal. PDE , 6: (1): 221--256
DOI: 10.2140/apde.2013.6.221
[7] Jens Kaad, Matthias Lesch
Spectral flow and the unbounded Kasparov product
Adv. Math. , 248: : 495--530
DOI: 10.1016/j.aim.2013.08.015
[8] Jens Kaad, Matthias Lesch
A local global principle for regular operators in Hilbert C*-modules
J. Funct. Anal. , 262: (10): 4540--4569
DOI: 10.1016/j.jfa.2012.03.002
[9] Matthias Lesch, Carolina Neira Jiménez
Classification of traces and hypertraces on spaces of classical pseudodifferential operators
J. Noncommut. Geom. , 7: (2): 457--498
DOI: 10.4171/JNCG/123
[10] Matthias Lesch, Boris Vertman
Regular singular Sturm-Liouville operators and their zeta-determinants
J. Funct. Anal. , 261: (2): 408--450
DOI: 10.1016/j.jfa.2011.03.011
[11] Matthias Lesch, Henri Moscovici, Markus J. Pflaum
Connes-Chern character for manifolds with boundary and eta cochains
Mem. Amer. Math. Soc. , 220: (1036): viii+92
ISBN: 978-0-8218-7296-3
DOI: 10.1090/S0065-9266-2012-00656-3
[12] Paul Kirk, Matthias Lesch
The η-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary
Forum Math. , 16: (4): 553--629
DOI: 10.1515/form.2004.027
[13] Matthias Lesch
On the noncommutative residue for pseudodifferential operators with log-polyhomogeneous symbols
Ann. Global Anal. Geom. , 17: (2): 151--187
DOI: 10.1023/A:1006504318696
[14] Jochen Brüning, Matthias Lesch
On the η-invariant of certain nonlocal boundary value problems
Duke Math. J. , 96: (2): 425--468
DOI: 10.1215/S0012-7094-99-09613-8
[15] Matthias Lesch
Operators of Fuchs type, conical singularities, and asymptotic methods
of Teubner-Texte zur Mathematik [Teubner Texts in Mathematics] : 190
Publisher: B. G. Teubner Verlagsgesellschaft mbH, Stuttgart
ISBN: 3-8154-2097-0
[16] Jochen Brüning, Matthias Lesch
On the spectral geometry of algebraic curves
J. Reine Angew. Math. , 474: : 25--66

Publication List

MathSciNet Publication List (external link)

ArXiv Preprint List (external link)



Gerhard-Hess Award, German Research Foundation (DFG)


Heisenberg fellowship, German Research Foundation (DFG)


NSF Grant DMS 0072551



Chair in Pure Math, Loughborough University, England, UK

Selected PhD students

Boris Vertman (2008): “The Analytic Torsion for Manifolds with Boundary and Conical Singularities”,
now Professor, University of Münster

Carolina Neira Jimenéz (2010): “Cohomology Of Classes Of Symbols And Classification Of Traces On Corresponding Classes Of Operators With Non Positive Order”,
now Assistant Professor, National University of Colombia

Batu Güneysu (2011): “On the Feyman-Kac formula for Schrödinger semigroups on vector bundles”,
now Postdoc, HU Berlin

Supervised Theses

  • Master theses: 5, currently 3
  • Diplom theses: 11
  • PhD theses: 8, currently 2
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