Homepage of Matthias Ludewig
I obtained my PhD from Universität Potsdam in 2016, under superivison of Christian Bär. Since October 2016 I am a postdoc at MPIM.
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.
Recent projects include:
- Feynman path integrals on manifolds, as well as their supersymmetric counterparts.
- Short-time asymptotic expansion of the heat kernel and geometric parametrices for elliptic and hyperbolic partial differential operators.
- Topological quantum field theory in the framework of S. Stolz and P. Teichner.
- The mass of conformal differential operators and their relation to the Yamabe invariant.
Below you find a list of my papers on the arxiv:
- Supersymmetric Path Integrals II: The Fermionic Integral and Pfaffian Line Bundles. Submitted. arXiv:1709.10028
- Supersymmetric Path Integrals I: Differential Forms on the Loop Space Submitted. arXiv:1709.10027
- The Trace and the Mass of subcritical GJMS Operators. Submitted. arXiv:1704.07218
- Asymptotic Expansions and Conformal Covariance of the Mass of Conformal Differential Operators. Submitted. arXiv:1612.02304
- Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional Determinants. Submitted. arXiv:1607.05891
- Strong Short Time Asymptotics and Convolution Approximation of the Heat Kernel. Submitted. arXiv:1607.05152
- Path Integrals on Manifolds with Boundary. Submitted. arXiv:1607.05151
- Asymptotic eigenfunctions for Schrödinger operators on a vector bundle, joint work with Elke Rosenberger. Submitted. arXiv:1309.4178
- A Semiclassical Heat Kernel Proof of the Poincare-Hopf Theorem. 2015. manuscripta math., Volume 148, Pages 29-58. arXiv:1302.6895
- Vector Fields with a non-degenerate Source. 2014. Journal of Geometry and Physics, Volume 79, Pages 59-76. arXiv:1308.3593
A survey on path integrals by finite-dimensional approximation:
My PhD thesis is available for download here:
- Path Integrals on Manifolds with Boundary and their Asymptotic Expansions. PhD thesis 2016. Download.