Hi, I'm Teresa Heiss,
a PhD student at
ISTA, and a co-director of the research network AATRN. Soon, I'll be a research fellow at ANU.


I'm a PhD student in the research group of Herbert Edelsbrunner at the Institute of Science and Technology Austria (ISTA), scheduled to graduate in fall 2024. Afterwards, I will move to Australia, for a MSI-Google Research Fellowship 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: 

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 current research, see my recorded talk at the IMSI workshop Randomness in Topology and Its Applications.

Other Activities

I'm a co-director of the Applied Algebraic Topology Research Network (AATRN) since 2021. Our >6500  YouTube subscribers and the feedback we get suggest that people really appreciate what we provide. We are very happy about that.
We are currently organizing an in-person workshop about applied topology at the IMSI institute in Chicago in August 2025 in celebration of the 10-year anniversary of AATRN. Please consider registering!

I was the math track students' representative at ISTA from 2021 to 2023.

I was a founding and executive committee member of the Austrian Association of Women in Mathematics (A²WiM) from 2020 to 2022.

I have co-organized the following activities:

I participate in several outreach activities, for example Zoom A Scientist, Zoom A Scientist Girls' Special, being a guest scientist at Talentesommer, giving interviews, ...

Together with my colleagues, we wrote lecture notes about Sheaf Theory and Applications

Together with my supervisor, Herbert Edelsbrunner, I taught a graduate level course on Computational Topology in 2019. 

I co-supervised the master thesis of Chiara Martyka (2022-2023), and the internships of  Dmitrii Vasilev (2019) and Sophie Rosenmeier (2023). It was a great pleasure to work with all three of them!

I created a tutorial about "Intuition for Persistent Homology Reduction Algorithm" with >1500 views on YouTube.





Get in touch at teresa (dot) heiss (at) ist (dot) ac (dot) at