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 MaxPlanckInstitute 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.
 Shorttime 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.
 Shorttime 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.
 Shorttime 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 2020 Ludewig, M., & Roos, S. (2020). The Chiral Anomaly of the Free Fermion in Functorial Field Theory. Annales Henri Poincare.
2019 Ludewig, M., & Rosenberger, E. (2019). Asymptotic eigenfunctions for Schrödinger operators on a vector bundle. Reviews in Mathematical Physics.
2019 Ludewig, M. (2019). Strong shorttime asymptotics and convolution approximation of the heat kernel. Annals of Global Analysis and Geometry, 55(2), 371394.
2018 Ludewig, M. (2018). Heat kernel asymptotics, path integrals and infinitedimensional determinants. Journal of Geometry and Physics, 131, 6688.
Scopus1 WoS12018 Ludewig, M. (2018). The trace and the mass of subcritical GJMS operators. Differential Geometry and its Application, 56, 95109.
2017 Ludewig, M. (2017). Path Integrals on Manifolds with Boundary. Communications in Mathematical Physics, 354(2), 621640.
Scopus1 WoS12017 Ludewig, M. (2017). Asymptotic expansions and conformal covariance of the mass of conformal differential operators. Annals of Global Analysis and Geometry, 52(3), 237268.
Scopus1 WoS12015 Ludewig, M. (2015). A semiclassical heat kernel proof of the Poincaré–Hopf theorem. Manuscripta Mathematica, 148(12), 2958.
2014 Ludewig, M. (2014). Vector fields with a nondegenerate source. Journal of Geometry and Physics, 79, 5976.
Scopus1 WoS1— Ludewig, M. (n.d.). Heat Kernels as Path Integrals. — Hanisch, F., & Ludewig, M. (n.d.). A Rigorous Construction of the Supersymmetric Path Integral Associated
to a Compact Spin Manifold.— Hanisch, F., & Ludewig, M. (n.d.). Supersymmetric Path Integrals II: The Fermionic Integral and Pfaffian
Line Bundles.— Güneysu, B., & Ludewig, M. (n.d.). The Chern Character of θsummable Fredholm Modules over dg
Algebras and Localization on Loop Space.— Ludewig, M., & Thiang, G. C. (n.d.). Good Wannier bases in Hilbert modules associated to topological
insulators.— Ludewig, M. (n.d.). Construction of the Supersymmetric Path Integral: A Survey. — Ludewig, M., & Stoffel, A. (n.d.). A framework for geometric field theories and their classification in
dimension one.— Ludewig, M., & Thiang, G. C. (n.d.). Cobordism invariance of topological edgefollowing states.
During my my PhD from 201216, I was funded by a scholarship of the Potsdam Graduate School.
I obtained a Fulbright scholarship to spend the semester 20132014 at Stanford University.
During my my PhD from 201216, I was funded by a scholarship of the Potsdam Graduate School.
I obtained a Fulbright scholarship to spend the semester 20132014 at Stanford University.
During my my PhD from 201216, I was funded by a scholarship of the Potsdam Graduate School.
I obtained a Fulbright scholarship to spend the semester 20132014 at Stanford University.
During my my PhD from 201216, I was funded by a scholarship of the Potsdam Graduate School.
I obtained a Fulbright scholarship to spend the semester 20132014 at Stanford University.
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