Research

Preprints

Moduli Spaces of Positive Curvature Metrics in Dimension Four and Beyond. arXiv:2310.14115

Line Bundles Twists for Unitary Bordisms are Ghosts. To appear in Algebr. Geom. Topol. arXiv:2202.09919

Concordances in Positive Scalar Curvature and Index Theory, PhD-Thesis, University of Göttingen (2022). arXiv:2303.07844
In my PhD thesis, I constructed with the help of cubical set theory, an "approximation space" to the space of positive scalar curvature metrics whose homotopy groups are precisely concordance classes of positive scalar curvature metrics. I further showed that the index difference factors through that space. To achieve this, I established a new model for the classifying space of real K-theory using invertible pseudo Dirac operators.
Pin Bordism in Low Degrees of Classifying Spaces, Master's-Thesis, University of Göttingen (2017). Available here
In my Master's Thesis I answered a question raised by Edward Witten what the fourth Pin bordism group of the classifying space BO(2) is. To achieve this, I modelled this classifying space as an infinite dimensional Dold-manifold and used the Atiyah-Hirzebuch spectral sequence to calculate the first five Pin bordism group of that space.