Homepage of Matthias Ludewig

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:


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

  1. Supersymmetric Path Integrals II: The Fermionic Integral and Pfaffian Line Bundles. Submitted. arXiv:1709.10028
  2. Supersymmetric Path Integrals I: Differential Forms on the Loop Space Submitted. arXiv:1709.10027
  3. The Trace and the Mass of subcritical GJMS Operators. Submitted. arXiv:1704.07218
  4. Asymptotic Expansions and Conformal Covariance of the Mass of Conformal Differential Operators. Submitted. arXiv:1612.02304
  5. Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional Determinants. Submitted. arXiv:1607.05891
  6. Strong Short Time Asymptotics and Convolution Approximation of the Heat Kernel. Submitted. arXiv:1607.05152
  7. Path Integrals on Manifolds with Boundary. Submitted. arXiv:1607.05151
  8. Asymptotic eigenfunctions for Schrödinger operators on a vector bundle, joint work with Elke Rosenberger. Submitted. arXiv:1309.4178
  9. A Semiclassical Heat Kernel Proof of the Poincare-Hopf Theorem. 2015. manuscripta math., Volume 148, Pages 29-58. arXiv:1302.6895
  10. 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: