Representations, Invariants, and Machine Learning in Knot Theory

09.06.2026, 12:15  –  Campus Golm, Building 9, Room 0.12
Forschungsseminar Angewandte Geometrie und Topologie

Djordje Mihajlovic (University of Edinburgh)

I will introduce the notion of using tools from computer science; specifically, machine learning (ML), to investigate problems in knot theory.  The central task is automated classification of different embeddings of S¹ in R³ (colloquially knots) up to ambient isotopy, and analysis of relationships between their invariant measures. To this end, ML tools may present a new regime for probing and helping us conjecture from mathematical data. We will discuss previous results in this field motivating our research, after which we show the process is not always trivial, specifically highlighting difficulties in ML interpretability and showing that `shortcuts’  can arise from spurious correlations in computationally generated data.