Dr Matthias Ludewig
|Position||Laureate Research Associate|
|Org Unit||School of 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. You can access it here.
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.
- Index Theory
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.
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Entry last updated: Wednesday, 17 Oct 2018
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