[6] | 'The small-scale limit of magnitude and the one-point property' (with M. Yoshinaga), arXiv:2312.14497, 2023 |

[5] | 'The reachability homology of a directed graph' (with R. Hepworth), arXiv:2312.01378, 2023 |

[4] | 'Iterated magnitude homology', arXiv:2309.00577, 2023 |

[3] | 'Magnitude, homology, and the Whitney twist', Homol. Homotopy Appl. 25(1):105–130, 2024; arXiv:2211.02520, 2022 |

[2] | 'The size and shape of things: magnitude, diversity, homology', PhD thesis, Edinburgh, 2022
This contains all of the material in [1], most of [3] and some of [4], plus a chapter discussing alternative ways to extend magnitude homology from finite to infinite metric spaces. |

[1] | 'The maximum entropy of a metric space' (with T. Leinster), Q. J. Math. 72(4):1271–1309, 2021 |

'Bigraded path homology and the magnitude-path spectral sequence' (with R. Hepworth) |

(Some titles link to slides. Talks in italics are forthcoming.)

04.2024 |
[Title TBC] |
Topology Seminar |
BIMSA, Beijing |

07.2023 | What is the shape of a network? | SIAM Minisymposium on Magnitude | Eindhoven |

05.2023 | (Two untitled talks) | Beyond Finite Sets—Homotopy Theory and Combinatorics | Copenhagen |

01.2023 | Magnitude homology of enriched groups | Topology Seminar | Aberdeen |

12.2022 | What are higher-order roles in social systems? | SYCO 10 | Edinburgh |

04.2022 | Magnitude homology, normed groups, and holes in the plane | Algebra, Geometry and Combinatorics Seminar | TU Dresden |

06.2021 | Magnitude homology and iterated enrichment | Postgraduate Forum | Lancaster |

05.2021 | Magnitude homology of semidirect products and "spheres" | MiaowMiaow Bi/Double-Categorical Seminar | Sheffield |

11.2020 | Maximum entropy, uniform measure | ML@CL Machine Learning Seminar | Cambridge |

06.2020 | Magnitude homology, from scratch | Pure Postgraduate Seminar | Southampton |

12.2019 | Diversity and magnitude | LMS Applied Algebra and Geometry Research Network | Oxford |

04.2019 | The magnitude and diversity of a metric space | TopApp Workshop | IST Austria |

12.2023 | Iterated magnitude homology | Magnitude 2023 | Osaka |

05.2022 | Magnitude homology in Euclidean space | PSSL 106 | Brno |

08.2021 | Magnitude homology and iterated enrichment | Category Theory 20–>21 | Genova |

06.2021 | Magnitude homology and iterated enrichment | Categories and Companions Symposium | Macquarie |

07.2019 | The maximum diversity of a compact metric space | Magnitude 2019 | Edinburgh |

11.2023 | Reachability homology and the magnitude-path spectral sequence | Topology Seminar | Osaka |

02.2023 | Magnitude, diversity, homology. A survey, with questions | Analysis Seminar | Edinburgh |

10.2021 | Return of the alley cats: 10 minutes of magnitude | The Categorical Late Lunch | Edinburgh |

08.2021 | What is a hole in a locally metric category? | The Categorical Late Lunch | Edinburgh |

11.2019 | Hochschild homology for enriched categories | Hodge Club | Edinburgh |

04.2019 | The magnitude of an enriched category | GEARS Seminar | Edinburgh |

03.2019 | Diversity: developments in the biology of mathematics | Hodge Club | Edinburgh |

01.2019 | Building complexes from point clouds | Persistent Homology Working Seminar | Edinburgh |

03.2018 | Commutative monads | Part III Seminar | Cambridge |