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.

With Guy Boyde (Southampton) and Aryan Ghobadi (QMUL) I am organising…

Topics in Category Theory: A Spring School, ICMS, Edinburgh, 11-13 March 2020

This Spring School will gather together junior researchers to learn about important themes in contemporary category theory, from experts and from each other. The focus is on aspects of pure category theory as they interact with other areas of geometry, topology and logic.

Three invited speakers will each present a three-hour mini-course, accessible to non-specialists, introducing an area of active research. There will also be short talks contributed by PhD students and postdocs, and a poster session.

Invited speakers Olivia Caramello (Grothendieck Toposes); Constanze Roitzheim (Model Categories and Higher Category Theory); Greg Stevenson (Derived and Triangulated Categories).

Join us! Pre-registration is open now.

Papers

The maximum entropy of a metric space (with Tom Leinster), arXiv:1908.11184

Abstract We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies generalise the Shannon and Rényi entropies of information theory.

We prove that on any space X, there is a single probability measure maximising all these entropies simultaneously. Moreover, all the entropies have the same maximum value: the maximum entropy of X. As X is scaled up, the maximum entropy grows; its asymptotics determine geometric information about X, including the volume and dimension. We also study the large-scale limit of the maximising measure itself, arguing that it should be regarded as the canonical or uniform measure on X.

Primarily we work not with entropy itself but its exponential, called diversity and (in its finite form) used as a measure of biodiversity. Our main theorem was first proved in the finite case by Leinster and Meckes.

Talks

Conferences and visits

Teaching

As a graduate teaching assistant in the School of Mathematics at Edinburgh, I have tutored or am tutoring the following courses.

Outreach and exchange

Sep 2019 — Performing Arts Forum, Saint-Erme-Outre-et-Ramecourt

Instructor at Mobilis in Mobili (led by Gabriel Catren)—a week-long workshop, addressed to non-scientists, introducing the history that led from the first axiomatic formulation of geometry in Euclid's Elements to Einstein's theory of special and general relativity. Presented a class^† on Euclidean and Cartesian geometry, and a workshop aimed at "discovering" Gaussian curvature and the Theorema Egregium.

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 was 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 and 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 JCMB 5621

Email firstname.lastname@ed.ac.uk

This page was last updated on 11 November 2019. ^†Photo by Christian Töpfner.