Ripser (Thesis Project)

Ripser is a topological data analysis tool originally developed by my thesis supervisor Prof. Ulrich Bauer implementing persistent homology. Simply speaking, persistent homology gives insights into the topological structure of filtered datasets (for instance time series), detecting generalized holes and their persistence with respect to the filtration.

For my master's thesis project I rebuilt Ripser from scratch and extended its functionality with two novel algorithms that implement persistent relative (co)homology among other methods in an attempt to improve runtime performance for large data sets. These algorithms were applied to SARS-CoV-2 genome data to detect potential gain-of-function mutations early in the time series data (see this paper for more details). I also improved tooling and created simple educational versions that forgo intricate optimizations.

The thesis itself contains the theoretical counterpart to the software and features a comprehensive, relatively self-contained exposition on the topic of persistent homology. It should be accessible to anyone with an elementary understanding of topology, algebra and category theory. My thesis received the best possible grade of 1.0, "passed with distinction".