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.

Teaching

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

Publications

Below you find a list of my papers on the arxiv:

1. Cobordism invariance of topological edge-following states, with G. Thiang, preprint, 2020; arXiv:2001.08339
2. A framework for geometric field theories and their classification in dimension one, with Augusto Stoffel, preprint, 2020; arXiv:2001.05721
3. The Chiral Anomaly of the Free Fermion in Functorial Field Theory, with S. Roos. Ann. Henri Poincare, 21:1191-1233, 2020; arXiv:1909.04212
4. Good Wannier bases in Hilbert modules associated to topological insulators, with G. Thiang, preprint, 2019; arXiv:1904.13051
5. The Chern Character of theta-summable Fredholm Modules over dg Algebras and the Supersymmetric Path Integral, with B. Güneysu, preprint, 2019; arXiv:1901.04721
6. A Rigorous Construction of the Supersymmetric Path Integral Associated to a Compact Spin Manifold, with Florian Hanisch, preprint, 2017; arXiv:1709.10027
7. The Trace and the Mass of subcritical GJMS Operators, Differential Geom. Appl., 56:95-109, 2018; arXiv:1612.02304
8. Asymptotic Expansions and Conformal Covariance of the Mass of Conformal Differential Operators, Ann. Global Anal. and Geom., 52(3):237-268, 2016; arXiv:1612.02304
9. Strong short-time asymptotics and convolution approximation of the heat kernel, Ann. Global Anal. Geom., 55(2):371-394, 2019; arXiv:1607.05152
10. Heat kernel asymptotics, path integrals and infinite-dimensional determinants, J. Geom. Phys., 131:66-88, 2018; arXiv:1607.05891
11. Path Integrals on Manifolds with Boundary, Comm. in Math. Phys. 354(2):621-640, 2016; arXiv:1607.05151
12. Asymptotic eigenfunctions for Schrödinger operators on a vector bundle, with E. Rosenberger. To appear in Rev. Math. Phys.; arXiv:1309.4178
13. A Semiclassical Heat Kernel Proof of the Poincare-Hopf TheoremMan. Math. 148:29-58, 2015; arXiv:1302.6895
14. Vector fields with a non-degenerate source, J. Geom. Phys. 79:59-76, 2014; arXiv:1308.3593

Surveys:

• Heat Kernels as Path Integrals, 2016. arxiv:1810.07898. Extended version of part of the chapter Geometric analysis on singular spaces with F. Bei, J. Brüning, B. Güneysu. In: Space - time - matter, De Gruyter, Berlin, 2018.
• Construction of the supersymmetric path integral: A survey, 2019; arXiv:1910.13019

My PhD thesis is available for download here:

• Path Integrals on Manifolds with Boundary and their Asymptotic Expansions. PhD thesis 2016. Download.

Contact

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