Research Interests
I mainly work on compactifications of symmetric spaces, especially using the horofunction/Busemann compactification. Based on this I am interested in comparisons of different types of such compactifications and relations between them.
Thesis
Both my Phd thesis (2021) and my Diploma thesis (2014) are concerned with the horofunction compacitification of finite-dimensional normed spaces and of symmetric spaces. In my diploma thesis I set up a criterion to characterize the topology of the compactified normed vector space by converging sequences in the case where the norm of the space is polyhedral. In my Phd thesis, I reformulated and extended this criterion to the general case in two dimensions and smooths norms in any dimensions. This result is then used to realize Satake and Martin compacitifications of symmetric spaces as horofunction compacitifications of that space with respect to an approriate norm. The thesis is partly based on the papers and preprints presented below.
Preprints
- Together with T. Haettel, C. Walsh and A. Wienhard (2018): Horofunction Compactifications of Symmetric Spaces
- Together with L. Ji (2016): Polyhedral Horofunction Compactification as Polyhedral Ball
Submitted Papers
Together with Lizhen Ji (2018): Toric varieties vs. horofunction compactifications of polyhedral norms
Talks and posters
- At the online conference NCNGT in 2021.
Title: "The horofunction compacitifications of symmetric spaces" - Poster at the EWM German Chapter Conference in Leipzig, 2019.
Title: "Horofunction Compactification of ℝn with Polyhedral Norms" - At the conference Perspectives on convex projective geometry in Sète, 2019.
Title: "Horofunction and Satake compactifications of symmetric spaces" - At the conference Geometric Analysis meets Geometric Topology in Heidelberg, February 2019.
Title: "Horofunction and Satake compactifications of symmetric spaces" - At the conference "Paroles aux jeunes chercheurs en géométries et groupes" in Strasbourg, November 2016.
Title: "Compactifications of Symmetric Spaces"
Workshop
Together with Petra Schwer from KIT, Karlsruhe (now in Magdeburg), and Anna Wienhard I organized a workshop on Compactifications of Buildings and Symmetric Spaces in Heidelberg, May 16-17, 2017.