# 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.

a PhD student at

ISTA, and a co-director of the research network AATRN. Soon, I'll be a research fellow at ANU.

## Research

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 summer 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:

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 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:

Several tutorial-a-thons for Topological Data Analysis -- We published an article about our first tutorial-a-thon in the AMS Notices Early Career Section.

Several AATRN poster sessions for Applied Topology

A workshop: Get-together and career advice for young mathematicians

The first two Austrian Days of Women in Mathematics

An interdisciplinary scientific symposium about climate change: Young Scientists Symposium 2020

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.

## Talks

## Past:

### Invited:

February 29, 2024: At the Dagstuhl-Seminar about Applied and Combinatorial Topology (Schloss Dagstuhl, Germany)

January 25, 2024: A seminar talk at the Computing Sciences Area of Berkeley Lab (Berkeley, USA)

January 18, 2024: A seminar talk at the Department of Chemical and Biological Engineering of the University of Wisconsin-Madison (online)

September 26, 2023: At the Computational Persistence Workshop 2023 (Purdue University, USA / online)

September 18, 2023: At the mini-symposium "Computational Topology and Geometry" at the Meeting of the Austrian Mathematical Society 2023 (Graz, Austria)

August 21, 2023: At the mini-symposium "Recovery and Robustness of Geometric Fingerprints for Point Clouds and Data" at ICIAM 2023 (Tokyo, Japan / online)

July 6, 2023: At the mini-symposium "Topological data analysis. Theory and applications" at the Nordic Congress of Mathematicians with EMS (Aalborg, Denmark)

May 9, 2023: At the Dagstuhl-Seminar about Topological Data Analysis and Applications (Schloss Dagstuhl, Germany)

March 23, 2023: At the IMSI workshop Randomness in Topology and Its Applications (Chicago, USA) (video available online)

May 19, 2022: A seminar talk at Lisbeth Fajstrup's group at Aalborg University (Aalborg, Denmark)

September 22, 2021: At the Applied Algebraic Topology Research Network (AATRN) seminar (online) (video available on Youtube)

July 1, 2021: At the Thematic Einstein Semester on Geometric and Topological Structure of Materials (online)

May 27, 2021: At the mini-symposium "Computational Geometry, Topology and Symmetry Meet Material Science" at SIAM Conference on Mathematical Aspects of Materials Science (online)

April 9, 2021: At the mini-symposium "Mathematics for Materials Science" at BMC-BAMC (online)

September 8, 2020: At the Mathematics and Computer Science for Material Innovation (MACSMIN) conference (online)

March 3, 2020: A seminar talk at Kathryn Hess’ group at EPFL (Lausanne, Switzerland)

January 16, 2020: A seminar talk at Michael Kerber’s group at TU Graz (Graz, Austria)

August 30, 2019: At the 13th meeting of the UK Network Applied Geometry and Topology (Liverpool, UK)

### Contributed:

August 18, 2022: At the Austrian TDA Meeting (Salzburg, Austria)

December 15, 2021: At the Workshop "Applications of Topological Data Analysis to Big Data" at IEEE International Conference on Big Data 2021 (online)

June 10, 2021: At SoCG 2021 (Symposium on Computational Geometry) (online)

April 29, 2021: At the IMSI workshop Topological Data Analysis (online) (video available online)

October 3, 2019: At the problem session of the BIRS-CMO workshop Soft Packings, Nested Clusters, and Condensed Matter (Oaxaca, Mexico)

April 26, 2019: At a Student workshop in Computational Topology (TopApp) (IST Austria, Austria)

August 23, 2017: At the International Conference on Computer Analysis of Images and Patterns (CAIP) (Ystad, Sweden)