A more substantial post is upcoming, but I wanted to get out this announcement for a conference I’m helping to organise, along with Roger Picken, João Faria Martins, and Aleksandr Mikovic. Its website: https://sites.google.com/site/hgtqgr/home has more details, and will have more as we finalise them, but here are some of them:
Workshop and School on Higher Gauge Theory, TQFT and Quantum Gravity
Lisbon, 10-13 February, 2011 (Workshop), 7-13 February, 2011 (School)
Description from the website:
Higher gauge theory is a fascinating generalization of ordinary abelian and non-abelian gauge theory, involving (at the first level) connection 2-forms, curvature 3-forms and parallel transport along surfaces. This ladder can be continued to connection forms of higher degree and transport along extended objects of the corresponding dimension. On the mathematical side, higher gauge theory is closely tied to higher algebraic structures, such as 2-categories, 2-groups etc., and higher geometrical structures, known as gerbes or n-gerbes with connection. Thus higher gauge theory is an example of the categorification phenomenon which has been very influential in mathematics recently.
There have been a number of suggestions that higher gauge theory could be related to (4D) quantum gravity, e.g. by Baez-Huerta (in the QG^2 Corfu school lectures), and Baez-Baratin-Freidel-Wise in the context of state-sums. A pivotal role is played by TQFTs in these approaches, in particular BF theories and variants thereof, as well as extended TQFTs, constructed from suitable geometric or algebraic data. Another route between higher gauge theory and quantum gravity is via string theory, where higher gauge theory provides a setting for n-form fields, worldsheets for strings and branes, and higher spin structures (i.e. string structures and generalizations, as studied e.g. by Sati-Schreiber-Stasheff). Moving away from point particles to higher-dimensional extended objects is a feature both of loop quantum gravity and string theory, so higher gauge theory should play an important role in both approaches, and may allow us to probe a deeper level of symmetry, going beyond normal gauge symmetry.
Thus the moment seems ripe to bring together a group of researchers who could shed some light on these issues. Apart from the courses and lectures given by the invited speakers, we plan to incorporate discussion sessions in the afternoon throughout the week, for students to ask questions and to stimulate dialogue between participants from different backgrounds.
Provisional list of speakers:
- Paolo Aschieri (Alessandria)
- Benjamin Bahr (Cambridge)
- Aristide Baratin (Paris-Orsay)
- John Barrett (Nottingham)
- Rafael Diaz (Bogotá)
- Bianca Dittrich (Potsdam)
- Laurent Freidel (Perimeter)
- John Huerta (California)
- Branislav Jurco (Prague)
- Thomas Krajewski (Marseille)
- Tim Porter (Bangor)
- Hisham Sati (Maryland)
- Christopher Schommer-Pries (MIT)
- Urs Schreiber (Utrecht)
- Jamie Vicary (Oxford)
- Konrad Waldorf (Regensburg)
- Derek Wise (Erlangen)
- Christoph Wockel (Hamburg)
The workshop portion will have talks by the speakers above (those who can make it), and any contributed talks. The “school” portion is, roughly, aimed at graduate students in a field related to the topics, but not necessarily directly in them. You don’t need to be a student to attend the school, of course, but they are the target audience. The only course that has been officially announced so far will be given by Christopher Schommer-Pries, on TQFT. We hope/expect to also have minicourses on Higher Gauge Theory, and Quantum Gravity as well, but details aren’t settled yet.
If you’re interested, the deadline to register is Jan 8 (hence the rush to announce). Some funding is available for those who need it.