Research interests

• The main focus of my research is on spectral analysis of filtered manifolds. More specifically, I am studying the analytic torsion of the Rumin complex for generic rank two distributions in dimension five, a.k.a. (2,3,5) distributions. Presently, I am applying methods form parabolic geometry to compute local quantities appearing in the small time asymptotic expansion of heat kernels associated with the Rumin complex, and I am using harmonic analysis on nilpotent Lie groups to relate the whole analytic torsion function of the Rumin complex on nilmanifolds to number theoretic properties of the corresponding lattice.


• I am also working on infinite dimensional groups of diffeomorphisms and their coadjoint orbits.

Research grants

• Analytic torsion of filtered manifolds (July 2019 -- July 2023), Grant DOI 10.55776/P31663, €160k, funded by the Austrian Science Fund (FWF)


• Torsion of manifolds (March 2007 -- February 2012), Grant DOI 10.55776/P19392, €147k, funded by the Austrian Science Fund (FWF)


• Differential Geometry and Lie groups (October 2006 - September 2009), Initiativkolleg (doctoral college) IK I008-N, €590k, funded by the University of Vienna
  Joint with Robert Beig, Dietrich Burde, Andreas Cap, Michael Kunzinger, Peter Michor, and Roland Steinbauer

ORCID

• https://orcid.org/0000-0002-7064-2215