- Developing a paradifferential calculus on manifolds with low-regular metrics along the lines of the work of Klainerman/Rodianski. In particular I want to apply this to the situation in Speck to lower the required regularity and to get a precise description of the solution at the blow-up time.
- With Ingo Witt: Dispersive- and Strichartz estimates on nilpotents Lie Groups.
- With Jozsef Lörinczi:
*Eigenvalues at the continuum edge for fractional Schrödinger operators*In preparation.

Most of my (mathematics) articles have preprint versions on arXiv.

- With Claudia Garetto and Michael Ruzhansky:
*Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II. Microlocal analysis*Submitted. arXiv. - With Claudia Garetto and Michael Ruzhansky:
*Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness*published in Mathematische Annalen, arXiv - With Claudia Garetto:
*Well-posedness of hyperbolic systems with multiplicities and smooth coefficients*, published in Mathematische Annalen, arXiv - With Daniele Del Santo and Marius Paicu:
*Backward uniqueness for parabolic operators with non-Lipschitz coefficients*, Osaka J. Math., Volume 52, Number 3 (2015), pp. 793-817 - With Daniele Del Santo and Martino Prizzi:
*Conditional stability for backward parabolic equations with $LogLip_t \times Lip_x$-coefficients*, Nonlinear Analysis: Theory, Methods & Applications, Volume 121, July 2015, pp. 101-122

- With Ayyoub Ahar, Tobias Birnbaum, and Peter Schalkens.
*A new similarity measure for complex amplitude holographic data*, Conference: SPIE Optical Engineering + Application, 6-10 August 2017 in San Diego, California, United States. doi: 110.1117/12.2274761. - With Ayyoub Ahar, Tobias Birnbaum, and Peter Schalkens.
*A New Similarity Measure for Complex Valued Data*, Conference: Digital Holography and Three-Dimensional Imaging 2017 JeJu Island South Korea 29 May – 1 June 2017. doi: 10.1364/DH.2017.Tu1A.6. -
*Note on backward uniqueness for a class of parabolic equations*. Published in a Proceedings of the Section Dispersion equations of the 10th Isaac congress. New Trends in Analysis and Interdisciplinary Applications, Springer, pp. 499-505. doi: 10.1007/978-3-319-48812-7_63, ISBN: 978-3-319-48810-3. - With Daniele Del Santo:
*Non-uniqueness and Uniqueness in the Cauchy Problem of Elliptic and Backward-Parabolic Equations*Published in a Proceedings of the Section Dispersion equations of the 9th Isaac congress. Progress in Partial Differential Equations, Springer Proceedings in Mathematics & Statistics, Vol. 44, 2013, pp. 27-52. ISBN: 978-3-319-00124-1