Matthias Ludewig

Dr Matthias Ludewig

Laureate Research Associate

School of Mathematical Sciences

Faculty of Engineering, Computer and Mathematical Sciences


I obtained my PhD from Universität Potsdam in 2016, under superivison of Christian Bär. During my doctorate, I also spend half a year at Stanford University, working with Rafe Mazzeo. The title of my thesis was "Path integrals on manifolds with boundary and their asymptotic expansions.

I was a postdoc at the Max-Planck-Institute for Mathematics in Bonn starting in October 2016, where my mentor was Peter Teichner.

In September 2018, I moved to the University of Adelaide as a Laureate Research Associate, to work with Mathai Varghese.

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 and interests include:

  • Index Theory
  • Functional 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 particular the framework of Stolz and Teichner, and the classification of topological phases by Freed and Hopkins.
  • The mass of conformal differential operators and their relation to the Yamabe invariant.

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 and interests include:

  • Index Theory
  • Functional 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 particular the framework of Stolz and Teichner, and the classification of topological phases by Freed and Hopkins.
  • The mass of conformal differential operators and their relation to the Yamabe invariant.

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 and interests include:

  • Index Theory
  • Functional 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 particular the framework of Stolz and Teichner, and the classification of topological phases by Freed and Hopkins.
  • The mass of conformal differential operators and their relation to the Yamabe invariant.
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  • Journals

    Year Citation
    2019 Ludewig, M. (2019). Strong short-time asymptotics and convolution approximation of the heat kernel. Annals of Global Analysis and Geometry, 55(2), 371-394.
    DOI
    2018 Ludewig, M. (2018). Heat kernel asymptotics, path integrals and infinite-dimensional determinants. Journal of Geometry and Physics, 131, 66-88.
    DOI
    2018 Ludewig, M. (2018). The trace and the mass of subcritical GJMS operators. Differential Geometry and its Application, 56, 95-109.
    DOI
    2017 Ludewig, M. (2017). Path Integrals on Manifolds with Boundary. Communications in Mathematical Physics, 354(2), 621-640.
    DOI Scopus1 WoS1
    2017 Ludewig, M. (2017). Asymptotic expansions and conformal covariance of the mass of conformal differential operators. Annals of Global Analysis and Geometry, 52(3), 237-268.
    DOI Scopus1 WoS1
    2015 Ludewig, M. (2015). A semiclassical heat kernel proof of the Poincaré–Hopf theorem. Manuscripta Mathematica, 148(1-2), 29-58.
    DOI
    2014 Ludewig, M. (2014). Vector fields with a non-degenerate source. Journal of Geometry and Physics, 79, 59-76.
    DOI Scopus1 WoS1
    Ludewig, M. (n.d.). Heat Kernels as Path Integrals.
    Hanisch, F., & Ludewig, M. (n.d.). Supersymmetric Path Integrals I: Differential Forms on the Loop Space.
    Hanisch, F., & Ludewig, M. (n.d.). Supersymmetric Path Integrals II: The Fermionic Integral and Pfaffian
    Line Bundles.
    Ludewig, M., & Rosenberger, E. (n.d.). Asymptotic eigenfunctions for Schrödinger operators on a vector bundle.
    Güneysu, B., & Ludewig, M. (n.d.). The Chern Character of θ-summable Fredholm Modules over dg
    Algebras and the Supersymmetric Path Integral.
    Ludewig, M., & Thiang, G. C. (n.d.). Good Wannier bases in Hilbert modules associated to topological
    insulators.

During my my PhD from 2012-16, I was funded by a scholarship of the Potsdam Graduate School.

I obtained a Fulbright scholarship to spend the semester 2013-2014 at Stanford University.

During my my PhD from 2012-16, I was funded by a scholarship of the Potsdam Graduate School.

I obtained a Fulbright scholarship to spend the semester 2013-2014 at Stanford University.

During my my PhD from 2012-16, I was funded by a scholarship of the Potsdam Graduate School.

I obtained a Fulbright scholarship to spend the semester 2013-2014 at Stanford University.

During my my PhD from 2012-16, I was funded by a scholarship of the Potsdam Graduate School.

I obtained a Fulbright scholarship to spend the semester 2013-2014 at Stanford University.

  • Position: Laureate Research Associate
  • Email: matthias.ludewig@adelaide.edu.au
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor 7
  • Room: 7 30
  • Org Unit: School of Mathematical Sciences

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