Research

My research centres on how to understand complex data sets, mostly in biomedical contexts, using (among other things) topological machine learning methods. I consider myself to be a toolsmith, creating new tools that help us deal with challenging problems.

If you are interested in topological machine learning, consider joining TDA in ML, a Slack community dedicated to discussing all things topological machine learning.

Publications

Please find a list of my preprints and publications below. Equal contributions by several authors are indicated using a superscript dagger symbol, i.e. . A superscript ‘double dagger’, or diesis, i.e. , denotes a publication that was jointly directed. I aim to provide a BibTeX file for citing the publication as well as the slides corresponding to the paper. If neither a preprint nor slides are available but you still want to read the publication, please drop me a line to bastian@rieck.me—it is possible that I am only allowed to share a publication privately.

Preprints

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

Notes

Here are some notes on various topics. These notes are not peer-reviewed, though, and may contain errors—please notify me if you find some.

Research interests

Our world is full of complex phenomena that happen at different temporal or spatial scales. I am interested in developing methods and techniques that help us understand these phenomena, especially in the presence of noisy or time-varying measurements.

Broadly speaking, this means that I have a penchant for developing new topological machine learning techniques, i.e. algorithms that are ‘aware’ of the fundamental topological properties of a data set. If you are familiar with machine learning terminology, this translates to developing new inductive biases and new architectures.

(I also have a general interest in algebraic & differential topology—both fields contain a wealth of potentially useful tools for visualisation and machine learning!)

Since ’theory without practice is empty,’ I also aim to build bridges to applications, in particular those that arise in the life sciences or healthcare in general. These domains are a source of complex data sets and challenges, and solutions to these challenges promise to have a profound, positive impact on society. As a mathematician-turned-computer-scientist-turned-something-else, this sparks immense joy and gratitude!

I am fortunate to work with many outstanding human beings, some of which also have personal websites: