Homepage of Matthias Ludewig

Publications


You can check out my profile on Google Scholar and my articles on the arxiv and on MathSciNet.


Preprints

arXiv Coarse geometric approach to topological phases: Invariants from real-space representations, with Christoph Setescak and Caio Lewenkopf.
arXiv Coarse geometry and its applications in solid state physics.
arXiv A representation of the string 2-group, with Peter Kristel and Konrad Waldorf.
arXiv Quantization of conductance and the coarse cohomology of partitions, with Guo Chuan Thiang.
arXiv The spinor bundle on loop space.
arXiv The stringor bundle, with Peter Kristel and Konrad Waldorf.
arXiv The insidious bicategory of algebra bundles, with Peter Kristel and Konrad Waldorf.
arXiv 2-vector bundles, with Peter Kristel and Konrad Waldorf.

Journal articles

arXiv Journal Lie 2-groups from loop group extensions, with Konrad Waldorf.
Journal of Homotopy and Related Structures , 2024
arXiv Journal Categories of Lagrangian correspondences and fermionic functorial field theory.
SIGMA 20, paper no. 036, 2024
arXiv Journal Large-scale geometry obstructs localization, with Guo Chuan Thiang.
J. Math. Phys. 63, paper no. 91902, 2022
arXiv Journal The Clifford algebra bundle on loop space.
SIGMA 20, paper no. 020, 2024
arXiv Journal Delocalized spectra of Landau operators on helical surfaces, with Yosuke Kubota and Guo Chuan Thiang.
Comm. Math. Phys. 395, pp 1211-1242, 2022
arXiv Journal Breaking symmetries for equivariant coarse homology theories, with Ulrich Bunke.
J. Geom. Phys. 201, paper no. 105214, 2024
arXiv Journal A Short Proof of the Localization Formula for the Loop Space Chern Character of Spin Manifolds, with Zelin Yi.
J. Noncommut. Geom. 17(1), pp 189-210, 2023
arXiv Journal Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry, with Guo Chuan Thiang.
Comm. Math. Phys. 386, pp 87-106, 2021
arXiv Journal Cobordism invariance of topological edge-following states, with Guo Chuan Thiang.
Adv. Theor. Math. Phys. 26(3), pp 673-710, 2022
arXiv Journal A framework for geometric field theories and their classification in dimension one, with Augusto Stoffel.
SIGMA 17, paper no. 072, 2021
arXiv Journal The Chiral Anomaly of the Free Fermion in Functorial Field Theory, with Saskia Roos.
Ann. Henry Poincaré 21, pp 1191-1233, 2020
arXiv Journal Good Wannier bases in Hilbert modules associated to topological insulators, with Guo Chuan Thiang.
J. Math. Phys. 61, paper no. 061902, 2020
arXiv Journal The Chern Character of theta-summable Fredholm Modules over dg Algebras and the Supersymmetric Path Integral, with Batu Güneysu.
Adv. Math. 395, paper no. 108143, 2021
arXiv Journal The Fermionic integral on loop space and the Pfaffian line bundle, with Florian Hanisch.
J. Math. Phys 63, paper no. 123502, 2022
arXiv Journal A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold, with Florian Hanisch.
Comm. Math. Phys 391, pp 1209-1239, 2022
arXiv Journal The Trace and the Mass of subcritical GJMS Operators.
Diff. Geom. Appl. 56, pp 95-109, 2018
arXiv Journal Asymptotic Expansions and Conformal Covariance of the Mass of Conformal Differential Operators.
Ann. Global Anal. and Geom. 52, pp 237-268, 2017
arXiv Journal Heat kernel asymptotics, path integrals and infinite-dimensional determinants.
J. Geom. Phys. 131, pp 66-88, 2018
arXiv Journal Strong short-time asymptotics and convolution approximation of the heat kernel.
Ann. Global Anal. Geom. 55, pp 371-394, 2019
arXiv Journal Path Integrals on Manifolds with Boundary.
Comm. in Math. Phys. 354, pp 621-640, 2017
arXiv Journal Asymptotic eigenfunctions for Schrödinger operators on a vector bundle, with Elke Rosenberger.
Rev. Math. Phys. 32(7), paper no. 2050020, 2020
arXiv Journal Vector fields with a non-degenerate source.
J. Geom. Phys 79, pp 59-76, 2014
arXiv Journal A Semiclassical Heat Kernel Proof of the Poincare-Hopf Theorem.
Manuscripta Math. 148, pp 29-58, 2015

Book Chapters

arXiv Coarse geometry and its applications in solid state physics.
To appear in: Encyclopedia of Mathematical Physics, 2nd Edition
arXiv Book Construction of the Supersymmetric Path Integral: A Survey.
In: Differential Geometry in the Large, Editors: Owen Dearricott, Wilderich Tuschmann, Yuri Nikolayevsky, Thomas Leistner, Diarmuid Crowley, Cambridge University Press, 2020
arXiv Book Heat Kernels as Path Integrals.
In: Space – Time – Matter, Editors: Jochen Brüning and Matthias Staudacher, de Gruyther, 2018

Thesis

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

Lecture notes

Link C*-Algebras and K-Theory
Link More Differential Geometry -- Addendum zum Skript Differential Geometry von Christian Bär