### Publications

- The category of opetopes and the category of opetopic sets. In Theory and Applications of Categories, 11:353–374, 2003. E-print math.CT/0304284
- Pseudo-distributive laws. With Martin Hyland and John Power, in Electronic Notes in Theoretical Computer Science, 83, 2004.
- Weak n-categories: opetopic and multitopic foundations. In Journal of Pure and Applied Algebra, 186(2):109–137, 2004. E-print math.CT/0304277
- Weak n-categories: comparing opetopic foundations. In Journal of Pure and Applied Algebra, 186(3):219–231, 2004. E-print math.CT/0304279
- A relationship between trees and Kelly-Mac Lane graphs. In Mathematical Proceedings of the Cambridge Philosophical Society, 141(1):33-56, 2006. E-print math.CT/0304287
- The periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories. With Nick Gurski. In Categories in Algebra, Geometry and Mathematical Physics, proceedings of Streetfest, editors Batanin et al, Contemporary Math. AMS 431:143-164, 2007. Also available here, and on the arXiv 0708.1178
- An omega-category with all duals is an omega groupoid. In Applied Categorical Structures, 15(4):439–453, 2007. Also available here.
- Towards an n-category of cobordisms. With Nick Gurski, 2006. In Theory and Applications of Categories, 18:274-302, 2007. E-print 0708.1178.
- Monad interleaving: a construction of the operad for Leinster’s weak omega-categories. In Journal of Pure and Applied Algebra, 214:809–821, 2009. Also available here.
- A note on Penon’s definition of weak n-category. (With Michael Makkai). In Cahiers de Topologie et Géométrie Différentielle Catégoriques, 50:83–101, 2009. E-print 0907.3961.
- Iterated distributive laws. In Mathematical Proceedings of the Cambridge Philosophical Society, 150(3):459–487, 2011. E-print 0710.1120.
- Comparing operadic theories of n-category, 2008, 47 pages. In Homotopy, Homology and Applications, 13(2):217–249, 2011. E-print 0809.2070.
- The periodic table of n-categories for low dimensions II: degenerate tricategories. (With Nick Gurski). 33 pages. In Cahiers de Topologie et Géométrie Différentielle Catégoriques 52:82–125, 2011. E-print 0706.2307.
- Distributive laws for Lawvere Theories, 2011. 36 pages. To appear in Algebra Universalis. E-print 1112.3076 .
- A direct proof that the category of 3-computads is not cartesian closed. 8 pages. Cahiers de Topologie et Géométrie Différentielle Catégoriques, 54:3-12 (2013). E-print 1209.0414.
- Cyclic multicategories, multivariable adjunctions and mates. (With Nick Gurski and Emily Riehl). Journal of K-Theory, 13(2):337-396, 2014. E-print 1208.4520
- Iterated icons. (With Nick Gurski). To appear in
*Theory and Applications of Categories.*E-print 1308.6495

**
Non-specialist** (for non-specialist preprints click here)

- Category theory. In The Princeton Companion to Mathematics, ed. Timothy Gowers et al, Princeton University Press, 2008.

Preprints

- Opetopic bicategories: comparison with the classical theory. Available via math.CT/0304285
- An alternative characterisation of universal cells in opetopic n-categories, 2002. Available via math.CT/0304286
- The theory of opetopes via Kelly-Mac Lane graphs, 2002. Available via math.CT/0304288
- Weak omega-categories via terminal coalgebras. (With Tom Leinster.) Available via 1212.5853 .

**Ph.D. thesis, supervised by Martin Hyland**

- Higher-Dimensional Category Theory: opetopic foundations, PhD thesis, University of Cambridge, March 2002. Available here.

Submitted book

- Higher dimensional categories: an illustrated guide book. With Aaron Lauda, 2004. Available here.

Slides from talks

- Terminal coalgebras. With Tom Leinster, 2008. Short version from CT08 (Calais), long version from PSSL87 (Patras).

### Conferences

**2017**

Empire Elixir, NYC 20 May, (Keynote speaker)

**2016**

Imaginary, Berlin 20-23 July, (Invited speaker)

Typelevel Summit, Oslo 4 May (Keynote speaker)

Compose conference, NYC 4-5 Feb (Keynote Speaker)

**2015**

CT2015, Aveiro, Portugal, 15-19 June

**2014**

CT2014, 29 June – 5 July, Cambridge

**2013**

British Mathematical Colloquium and extraordinary PSSL 94, 25-28 March, University of Sheffield (an event I am co-organising with David Jordan)

CT2013 (invited speaker), 7-13 July, Macquarie University and satellite workshop 2-5 July

**2012**

PSSL 93, 14-15 April 2012, Cambridge

**2011**

ScotCats 4, 13 May 2011 (invited speaker), Glasgow

Category Theory, Algebra and Geometry, 26-27 May 2011 (invited speaker), Louvain-la-Neuve, Belgium

CT2011, 17-23 July UBC, Vancouver

**2010**

Categories, Logic and Foundations of Physics VI, March 9 2010 Oxford, UK

PSSL 90, 24-25 April 2010, Braunschweig, Germany

CT2010, 20-26 June 2010, Genova, Italy

PSSL 91, 28-29 November 2010, Amsterdam, Netherlands

**2009**

Categories, Logic and Foundations of Physics IV, January 7 2009 (invited speaker) Imperial College, London

The 88th Peripatetic Seminar on Sheaves and Logic This is a conference I organised in honour of the joint 60th birthdays of Martin Hyland and Peter Johnstone in Cambridge, April 2009.

PSSL 89, 12-13 December 2009, Louvain-la-Neuve, Belgium

**2008**

Categories, Logic and Foundations of Physics I, January 9 2008 Imperial College, London

PSSL 87, March 21-23 2008 Patras, Greece

Categories, Logic and Foundations of Physics II, May 14 2008 Imperial College, London

CT2008, June 22-28 2008 Calais, France

HOCAT 08, June 30-July 5 2008 Barcelona, Spain

ATMCS 2008, July 7-11 2008 Paris 7, France

**2007**

Fields Institute: Thematic Program on Geometric Applications of Homotopy Theory 2007

I co-organised the subprogram: Higher categories and their applications – Jan/Feb 2007

Workshop January 9-13

The 85th Peripatetic Seminar on Sheaves and Logic This is a conference I organised in Nice in March 2007

SECA4, June 6-9 2007 (invited speaker) Barcelona, Spain

CT2007, June 17-23 2007 Carvoeiro, Portugal

**2006**

Alpine Operad workshop, March 2006 (invited speaker)

Mac Lane memorial conference, April 2006 This is a conference I co-organised in Chicago in April 2006

CT2006, July 2006 White Point, Nova Scotia

**2005**

Streetfest, July 2005

Octoberfest 2005, Ottawa

Union College Conference, December 2005

**2004**

The 80th Peripatetic Seminar on Sheaves and Logic This is a conference I co-organised in Cambridge in April 2004

IMA workshop on Higher Categories and their Applications, Minneapolis, June 7-18

CT2004, UBC, Vancouver, July

**2003**

PSSL 79, June 28-29, Doorn, Netherlands

MFPS 19, March 19-22, Montreal, Canada

PSSL 78, Feb 15-16, Strasbourg, France

**2002**

PSSL 77, Oct 5-6, Braunschweig, Germany

PSSL 76, Mar 2-3, Copenhagen, Denmark

**2001**

PSSL 75, June 9-10, Stockholm, Sweden

**2000**

PSSL 74, Nov 4-5, Cambridge, UK

CT2000, July 16-22, Como, Italy

PSSL 73, Apr 29-30, Braunschweig, Germany

**1999**

PSSL 73, Oct 16-17, Louvain-la-Neuve, Belgium

PSSL 71, Feb 27-28, Cambridge, UK