[Image] Emily Roff

I am a PhD student at the University of Edinburgh, working with Tom Leinster. I'm a member of the Geometry and Topology group in the Hodge Institute, and my primary research interests are in category theory and its applications.

Before joining the University of Edinburgh in September 2018 I took the MASt in Pure Mathematics at the University of Cambridge, where I wrote my Part III essay under the supervision of Martin Hyland. Before that, I studied for a BSc with the Open University and King's College London.


The maximum diversity of a compact space, with Tom Leinster, in preparation (provisional title, spring 2019).

We define a family (Dq)q ∈ [-∞,+∞] of `similarity-sensitive' indices of entropy for probability measures on a compact Hausdorff topological space; these are referred to as diversity indices, because their definition in the finite setting was first motivated by problems in mathematical ecology. We show that every compact Hausdorff space that's equipped with a suitable notion of (dis-)similarity of points (for instance, a metric) admits a probability measure which maximises the order-q diversity for infinitely many q at once. The maximum diversity of such a space is seen to be a well-defined numerical invariant, closely related both to the magnitude of a metric space—a direct descendent of the Euler characteristic of a category—and, via a result of Mark Meckes's, to Minkowski dimension. Studying diversity-maximising measures on a metric space as its metric is scaled, we also obtain something like a canonical uniform measure on a wide class of compact metric spaces.


Jul 2019 The maximum diversity of a compact metric space Magnitude 2019, ICMS, Edinburgh
Apr 2019 The magnitude and diversity of a metric space TopApp workshop, IST Austria
Apr 2019 The magnitude of an enriched category GEARS seminar, Edinburgh/Glasgow
Mar 2019 Diversity: developments in the biology of mathematics Hodge Club, Edinburgh
Jan 2019 Building complexes from point clouds Persistent homology working seminar, Edinburgh
Mar 2018 Commutative monads Part III seminar, Cambridge

Conferences and visits

Jul 2019 Category Theory 2019, Edinburgh
Jul 2019 Magnitude 2019: Analysis, Category Theory, Applications, Edinburgh
May 2019 PSSL 105, Palermo
May 2019 Visiting Universitat Autònoma de Barcelona
Apr 2019 TopApp workshop on applied and computational topology, IST Austria
Oct 2018 The Philosophy and Physics of Noether's Theorems, London

Outreach and exchange

Nov 2018, May 2019 — Robert Schumann Hochschule, Düsseldorf
Invited participant at Form and Formalism (led by Julian Rohrhuber and Tzu Chien Tho)—a seminar for students of music informatics and media theory with an interest in abstract algebra and category theory. Led discussions about universal properties, diagrams and limits.
Jun 2018 — Performing Arts Forum, Saint-Erme-Outre-et-Ramecourt
Instructor at Categories for the Hard-Working Non-Mathematician (led by Gabriel Catren)—a week-long, philosophically oriented introduction to the basics of category theory for people without a university background in mathematics. Presented three two-hour lectures: on sets, equivalence relations and groupoids; on categories and functors; and on algebraic methods in topology.
Feb 2018 — Skowhegan Gallery and NYU, New York
Invited participant at the Institute of Physical Sociality—a research group interested in mathematics and physics, ethics, gender and race, organised by Arika and led by Karen Barad, Gabriel Catren, Fred Moten and Fernando Zalamea.

Past lives

From 2011 through 2016 I worked as a welfare rights adviser with Child Poverty Action Group, Drumchapel Money Advice Centre, and WestGAP. Before that, I worked as a producer of music and arts projects with Arika and Tracer Trails. I have an undergraduate degree from the School of Scottish Studies at the University of Edinburgh, which involved training in anthropological theory and ethnographic research methods.

As my outreach / exchange activities suggest, I'm interested in talking with non-mathematicians about what mathematics has to do with understanding the social world, and I'm a fan of pedagogical experiments that aim to make such conversations possible.

Contact details

Office: Room 5.33, Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT

Email: firstname.lastname@ed.ac.uk

This page was last updated on 17 June 2019.