Welcome!
This is the official homepage of the workshop series Categories, Logic and Foundations of Physics. These workshops bring together researchers from the fields mentioned in the title and promote research on structural and conceptual aspects of fundamental physical theories, operational methodologies for general physical theories, as well as the general study of mathematical structures describing dynamics and space-time.
Please feel free to contact the workshop organizers if you have any questions, or if you want to attend one of our meetings.
- Bob Coecke, University of Oxford
- Andreas Doering, Imperial College London
There have been four workshops so far (9th January 2008, 14th May 2008, and 23rd/24th August 2008, 7th January 2009). We intend to keep an informal atmosphere for the workshops, with no formal registration, and strongly encourage interaction and discussions between the participants.
Previous event: 4th CLP Workshop, 7th January 2009, Imperial College, London
The fourth workshop on "Categories, Logic and Foundations of Physics" (CLP) took place at Imperial College on Wednesday, 7th January 2009, 11:00 - 19:00, Lecture Theatre 2, Blackett Laboratory.
Click here to watch the videos of this event.
We want to thank our speakers again for giving such excellent and informative talks, and all participants for coming to London. Thanks also go to Caroline Walker, the Group Coordinator of the Theoretical Physics Group at Imperial, and to Jamie Vicary, who videoed the talks.
This time, the focus was mainly on n-categories and related fields. The schedule was as follows:
- 11:00-12:00: Tom Leinster, An introduction to
-categories - I will give an beginners' introduction to -categories. First I'll explain roughly what an -category is, and talk about some of the dreams that first led people to want to develop a theory of -categories. Then I'll go into more detail, leading up to a description of the state of the art and of some of the difficulties involved in trying to make those dreams come true. This is a completely introductory talk, for those who know nothing about -categories. Experts will be bored senseless.
- 12:00-13:00: Eugenia Cheng, The Periodic Table of -categories - Degenerate -categories are those whose lowest
dimensions are trivial, for some 
. These can be thought of as the categorical analogue of loop spaces. The resulting multiplicative structures are interesting in their own right, and fit into a table known as the “Periodic table of -categories”. The table has various interesting patterns observable in low-dimensions and conjectured in general by Baez and Dolan. The structures that arise in this way include monoids and commutative monoids, as well as monoidal, braided, and symmetric monoidal categories. We will outline the main ideas behind the Periodic Table, its patterns and predictions, including the crucial stabilisation property which lead Baez and Dolan to conjecture a beautiful universal property to characterise higher-dimensional tangles. The talk will be introductory, in some sense a sequel to Tom Leinster's introduction to -categories that precedes it. Beyond this no knowledge of -categories will be assumed.
- 13:00-14:00: Lunch break (in Common Room on Level 8)
- 14:00-15:00: Ieke Moerdijk, Infinity categories and infinity operads - We discuss some aspects of the simplicial theory of infinity-categories which originates with Boardman and Vogt, and has recently been developed by Joyal, Lurie and others. The main purpose of the talk will be to present an extension of this theory which covers infinity-operads. It is based on a modification of the notion of simplicial set, called “dendroidal set”. One of the main results is that the category of dendroidal sets carries a monoidal Quillen model structure, in which the fibrant objects are precisely the infinity-operads, and which contains the Joyal model structure for infinity-categories as a localization. The lecture is partly based on joint work with Ittay Weiss, Clemens Berger, and Denis-Charles Cisinski.
- 15:00-16:00: Eric Paquette, Topological Quantum Computing with Anyons - In nature one observes that in three space dimensions particles are either symmetric or antisymmetric under interchange. In two dimensions, however, a whole continuum of phases is possible; "Anyon" is a term that describes quasi-particles in 2 dimensions that can acquire any phase when two or more of them are interchanged. Such peculiar property permits one to encode information in topological features of a system composed of many anyons. It has been suggested that such topological excitations could be used for robust quantum computation.
- 16:00-16:45: Tea break (in front of Lecture Theatre 2)
- 16:45-17:45: Edwin Beggs, Integrability, gravity and categories
- 17:45-18:45: Isar Stubbe, Principally generated modules on a quantale - Let
be a quantale, and 
the locally ordered category of -modules and -module morphisms. Using splittings of idempotents and adjunctions in , I shall define the 'principal elements' of a given -module; a 'principally generated' -module is then one "with enough principal elements". Applying this to a module over the two-element chain, i.e. a complete lattice, will give a familiar notion. I shall explain how, in general, this is related to the theory of ordered (!) sheaves over . When is moreover involutive, it makes sense to speak of ‘principally symmetric’ -modules; this then is related to sheaves over . Time permitting, I shall say a word or two on 'Hilbert -modules' too.
Best regards,
Andreas Doering (Imperial) and Bob Coecke (Oxford)
About this site - the video archive
This site went live on 11th December 2007. Feedback is very welcome. One of the most important features of this site is an extensive archive of over 50 recorded talks relevant to categories, logic and the foundations of physics, given by over 40 different speakers at different events around the world. You can browse these talks by speaker or by event, you can download or stream the videos, and download the slides where available.
We are constantly adding new talks, so make sure to check back often!
