Tom Leinster

Publications
Talks
Notes
Teaching


I'm a mathematician at the University of Glasgow, funded by the EPSRC.

Latest: 

New post at the n-Category Café: An adventure in analysis
New paper on the arXiv: A maximum entropy theorem with applications to the measurement of biodiversity
The Scottish Category Theory Seminar has its first meeting here in Glasgow on Friday 27 November

 

Publications

 

My book, Higher Operads, Higher Categories, is available free on the web and published in traditional form by Cambridge University Press. Summary and further information.

Here are my papers, grouped by subject. Within each subject, the most recent are listed first. You can also read an old overview of my papers up to about 2003.

Cardinality and Euler characteristic:

A maximum entropy theorem with applications to the measurement of biodiversity, arXiv:0910.0906, 27 pages, 2009
On the asymptotic magnitude of subsets of Euclidean space (with Simon Willerton), arXiv:0908.1582, 20 pages, 2009, submitted; discussion
The Euler characteristic of a category as the sum of a divergent series (with Clemens Berger), arXiv:0707.0835, 11 pages, 2007; also Homology, Homotopy and Applications 10 (2008), 41–51; discussion
The Euler characteristic of a category, math.CT/0610260, 2006; also Documenta Mathematica 13 (2008), 21–49; nice description here and discussion here and here

Self-similarity and recursion:

General self-similarity: an overview, math.DS/0411343, 10 pages, 2004; also in Real and Complex Singularities (Proceedings of the Australian-Japanese Workshop, Sydney, 2005), World Scientific (2007)
A general theory of self-similarity II: recognition, math.DS/0411345, 28 pages, 2004, submitted
A general theory of self-similarity I, math.DS/0411344, 49 pages, 2004, submitted
Objects of categories as complex numbers (with Marcelo Fiore), math.CT/0212377, 13 pages, 2002; also Advances in Mathematics 190 (2005), 264-277
An objective representation of the Gaussian integers (with Marcelo Fiore), math.RA/0211454, 6 pages, 2002; also Journal of Symbolic Computation 37 (2004), no. 6, 707-716

Category theory in algebra:

A simple description of Thompson's group F (with Marcelo Fiore), math.GR/0508617, 14 pages, 2005, accepted by Semigroup Forum
Are operads algebraic theories?, math.CT/0404016, 2004; also Bulletin of the London Mathematical Society 38 (2006), no. 2, 233-238

Higher-dimensional category theory:

A survey of definitions of n-category, math.CT/0107188, 67 pages, 2001; also Theory and Applications of Categories 10 (2002), no. 1, 1-70
Topology and higher-dimensional category theory: the rough idea, math.CT/0106240, 15 pages, 2001
Operads in higher-dimensional category theory (PhD thesis), math.CT/0011106, viii + 127 pages, 2000; also Theory and Applications of Categories 12 (2004), no. 3, 73-194
Generalized enrichment of categories, math.CT/0204279, 18 pages, 1999; also Journal of Pure and Applied Algebra 168 (2002), no. 2-3, 391-406
fc-multicategories, math.CT/9903004, 8 pages, 1999
Generalized enrichment for categories and multicategories, math.CT/9901139, 79 pages, 1999
Basic bicategories, math.CT/9810017, 11 pages, 1998
Structures in higher-dimensional category theory, math.CT/0109021, 81 pages, 1998
General operads and multicategories, math.CT/9810053, 35 pages, 1997

(Polished versions of most of the material in these unpublished papers can be found in my book.)

Homotopy algebra:

Homotopy algebras for operads, math.QA/0002180, 101 pages, 2000
Up-to-homotopy monoids, math.QA/9912084, 8 pages, 1999

Miscellaneous:

Perfect numbers and groups, math.GR/0104012, 12 pages, 1996ish; associated Sloane's integer sequence

The references above are to the electronic mathematics archive. For faster downloading, or if the links above aren't working, try a mirror site near you: Australia, Brazil, China, France, Germany, India, Russia, Spain, UK.

 

Talks

 

Here are slides and notes from some talks, grouped by subject. Within each subject, the most recent are listed first.

Cardinality and Euler characteristic:

Size (for a pure-mathematical audience, mostly model theorists)
Counting, measure and metrics (for a general mathematical audience)
How to measure almost anything (for a general scientific audience)
The cardinality of a metric space (shorter)
The cardinality of a metric space (longer)
New perspectives on Euler characteristic (for a general mathematical audience)
The Euler characteristic of a category (for category theorists)
Another look at Euler characteristic (for a general pure-mathematical audience)

Self-similarity and recursion:

Terminal coalgebras via modules
Coalgebraic topology
Periodicity of spaces of walks
Jónsson-Tarski toposes
Self-similarity and recursion
A universal Banach space

Category theory in algebra:

The Thompson groups
Nerves of algebras (see also this discussion)

Higher-dimensional category theory:

Introduction to higher (especially globular) operads
A survey of the theory of bicategories
Operads (90-minute tutorial)
Higher-dimensional algebra (for politicians)

Mathematics in general:

The power of abstract thinking (for prospective Ph.D. students)
The peculiar traits of human mathematics

Other talk-related things:

The Scottish Category Theory Seminar
Extremely short introduction to Beamer (a package that allows you to prepare pdf talk slides in Latex)
Conference in celebration of the 60th birthday of my PhD supervisor, Martin Hyland
The 2008 Rankin Lectures, given in Glasgow by John Baez
Tips on giving talks (ps, pdf)
The 83rd Peripatetic Seminar on Sheaves and Logic (held here in 2006); includes some notes from the talks
Category theory seminars in Cambridge, 1996-2002

 

Notes

 

I'm one of the hosts of The n-Category Café, a research blog on mathematics, physics and philosophy. Here are my posts (most recent first):

An adventure in analysis
Asymptotics of the magnitude of metric spaces
Entropy, diversity and cardinality (part 2)
Entropy, diversity and cardinality (part 1)
The cardinality of a metric space
How I learned to love the nerve construction
On Linear Algebra Done Right

Here are a couple of my comments at the n-Category Café:

A short explanation of the Central Limit Theorem and how to view it as a result about maximum entropy
Informal introduction to classifying toposes

And here are some odds and ends:

An interview with me in the December 2008 issue of The Reasoner, largely about higher categories
Doing without diagrams: how to take a proof that uses elements, utter some magic words, and conclude that it's valid in any category
A proof that sheaves do not belong to algebraic geometry
My favourite proof of the Fundamental Theorem of Algebra: argument learned from Graeme Segal and notes extracted from a course I taught

 

Teaching

 

Glasgow M.Sci. Category Theory 2007-8
Glasgow 4H Galois Theory 2005-6
Glasgow Category Theory 2004
Common errors in first year undergraduate work
Cambridge Part III Category Theory 2000
Cambridge Part IA/IB Linear Maths: some notes on the minimal polynomial and Jordan canonical form

 

Email: 'T.Leinster', followed by the at sign, followed by 'maths.gla.ac.uk'

This page was last changed on 4 November 2009. Photo.