Homepage of Matthias Ludewig

I am a PostDoc at the University of Regensburg in the group of Bernd Ammann.

I am interested in the geometry and topology of manifolds, and relations between the two. Here, much of my research is inspired by techniques, principles and heuristics from mathematical physics. In my research, I try to combine theory and techniques from areas like differential geometry, global and geometric analysis, geometric asymptotics and stochastic analysis on manifolds but also from homotopy theory and higher category theory.

My profile on Google Scholar and my articles on arxiv.

Research Seminars

Oberseminar Globale Analysis

Arbeitsgruppenseminar Ammann

Wochenprogramm Fakultät für Mathematik


Vorlesung "Differential Geometry II / Index Theory" (SS 2023): Link

Vorlesung "Differential Geometry I" (WS 2022/23): Link

Vorlesung "Analysis III für Physiker" (WS 2021/22): Link

Seminar "Lie groups, Lie algebras and their representations" (WS2020/21): Link

Lecture "C*-Algebras and K-Theory" (SS2020): Link



arXiv Categories of Lagrangian correspondences and fermionic functorial field theory.
arXiv A representation of the string 2-group, with P. Kristel and K. Waldorf.
arXiv The insidious bicategory of algebra bundles, with P. Kristel and K. Waldorf.
arXiv The Clifford algebra bundle on loop space.
arXiv Breaking symmetries for equivariant coarse homology theories, with U. Bunke.
arXiv 2-vector bundles, with Peter Kristel and Konrad Waldorf.

Journal articles

arXiv Cobordism invariance of topological edge-following states, with G. C. Thiang.
Accepted for publication in Advances of Theoretical and Mathematical Physics (ATMP).
arXiv A Short Proof of the Localization Formula for the Loop Space Chern Character of Spin Manifolds, with Z. Yi.
Accepted for publication in J. Noncommutative Geom.
arXiv Journal The Fermionic integral on loop space and the Pfaffian line bundle, with F. Hanisch.
J. Math. Phys. 63, 123502, 2022
arXiv Journal Delocalized spectra of Landau operators on helical surfaces, with Y. Kubota and G. C. Thiang.
Comm. Math. Phys. 395:1211-1242, 2022
arXiv Journal Large-scale geometry obstructs localization, with G. C. Thiang.
Journal of Mathematical Physics 63, 091902, 2022
arXiv Journal A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold, with F. Hanisch.
Comm. Math. Phys. 391:1209-1239, 2022
arXiv Journal The Chern Character of theta-summable Fredholm Modules over dg Algebras and the Supersymmetric Path Integral, with B. Güneysu.
Adv. Math. 395, 2022, Paper No. 108143, 2022
arXiv Journal A framework for geometric field theories and their classification in dimension one, with A. Stoffel.
SIGMA 17, 2021
arXiv Journal Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry, with G. C. Thiang.
Comm. Math. Phys., 386, 2021
arXiv Journal Good Wannier bases in Hilbert modules associated to topological insulators, with G. C. Thiang.
J. Math. Phys., 61, 061902, 2020
arXiv Journal The Chiral Anomaly of the Free Fermion in Functorial Field Theory, with S. Roos.
Ann. Henri Poincare, 21:1191-1233, 2020
arXiv Journal Asymptotic eigenfunctions for Schrödinger operators on a vector bundle, with E. Rosenberger.
Rev. Math. Phys. 37(7), 2050020, 2020
arXiv Journal Strong short-time asymptotics and convolution approximation of the heat kernel.
Ann. Global Anal. Geom., 55(2):371-394, 2019
arXiv Journal The Trace and the Mass of subcritical GJMS Operators.
Differ. Geom. Appl., 56:95-109, 2018
arXiv Journal Heat kernel asymptotics, path integrals and infinite-dimensional determinants.
J. Geom. Phys., 131:66-88, 2018
arXiv Journal Asymptotic Expansions and Conformal Covariance of the Mass of Conformal Differential Operators.
Ann. Global Anal. and Geom., 52(3):237-268, 2016
arXiv Journal Path Integrals on Manifolds with Boundary.
Comm. in Math. Phys. 354(2):621-640, 2016
arXiv Journal A Semiclassical Heat Kernel Proof of the Poincare-Hopf Theorem.
Man. Math. 148:29-58, 2015
arXiv Journal Vector fields with a non-degenerate source.
J. Geom. Phys. 79:59-76, 2014

Book Chapters

arXiv Book Construction of the supersymmetric path integral: A survey.
In: Differential Geometry in the Large, Ed. O. Dearricott, W. Tuschmann, Y. Nikolayevsky, T. Leistner, D. Crowley. Cambridge University Press, 2020
arXiv Book Heat Kernels as Path Integrals.
Part of the chapter Geometric analysis on singular spaces, with F. Bei, J. Brüning, B. Güneysu.
In: Space - time - matter, Ed. J. Brüning, M. Staudacher. De Gruyter, Berlin, 2018


Link Path Integrals on Manifolds with Boundary and their Asymptotic Expansions, 2016.

Lecture notes

Link C*-Algebras and K-Theory


My E-mail address is MyFirstName.MyLastname (at) mathematik.uni-regensburg.de