I completed my PhD in the research group of Herbert Edelsbrunner at the Institute of Science and Technology Austria (ISTA). Now, I am an MSI-Google Research Fellow at the Mathematical Data Science Centre at the Australian National University (ANU). I will be searching for graduate and undergraduate students to supervise in Canberra (and postdocs if I find funding for them), so please let me know if you are interested or know someone who is interested!
My research interests lie in Applied Algebraic Topology and Computational Geometry and include:
Persistent homology
Periodic point sets and lattices
Multifold persistent homology, also known as higher order (Delaunay) persistent homology
Applications to material science, for example crystalline materials
Brillouin zones, higher order Delaunay mosaics, higher order Voronoi tessellations
Digital images and cubical data
Topological Data Analysis (TDA)
Currently I'm investigating how to define persistent homology for periodic point sets, in a useful way (for example it should be invariant under the choice of representation of the periodic point set, stable under perturbations, and instead of yielding multiplicities of value infinity it should quantify how fast they grow). Additionally I'm searching for so-called crystal fingerprints that characterize crystalline materials uniquely and continuously. I'm also collaborating with Lisbeth Fajstrup and others on applying TDA to improve efficiency of glass batteries. With Alexey Garber and others, I have a series of three more theoretical papers on flips in hypertriangulations and other topics inspired by higher order Delaunay mosaics and Brillouin zones. Before that, I had various projects (with Hubert Wagner, Vanessa Robins, and others) about persistent homology and Euler characteristic curves of images.
My google scholar profile can be found here.
For a video of a my latest research project, see my recorded talk at the 2025 ICERM workshop Geometry of Materials.