Representations, Invariants, and Machine Learning in Knot Theory

Sun, 07 Jun 2026 00:00:00 +0000

Date: 09. June 2026

Location: Campus Golm, Building 9, Room 0.12

Speaker: Djordje Mihajlovic (University of Edinburgh)

Abstract:

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 \(S^1\) in \(\mathbb{R}^3\) (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.

Formalising Mathematics: Differential Geometry and Number Theory in the Lean Proof Assistant

Wed, 17 Dec 2025 00:00:00 +0000

This institute colloquium featured two talks on formalising mathematics in the Lean proof assistant.

Speakers: María Inés Frutos Fernández and Michael B. Rothgang (University of Bonn)

Michael Rothgang: Formalising differential geometry in Lean
María Inés de Frutos Fernández: Number Theory in the Lean Theorem Prover