**On generating series of classical spin networks**

Prof. Dr. Francesco Costantino's talk

Date: 26.05.11 Time: 10.00 - 10.50 Room: Gwatt Zentrum

Coauthor: Julien Marché, Université de Paris VI

**Abstract:**After recalling the definition of classical spin networks, I will state and discuss a nice result of Bruce Westbury which computes the generating series of these objects in the case of planar graphs. I will then recall a natural gauge-theoretical generalization of classical spin networks to include SL2(C)-valued holonomies, and relate these objects to character varieties of punctured surfaces. Then I will state a new result which computes the generating series for spin networks with holonomies (also for non-planar graphs) and relate this to a natural basis for the regular functions on the character variety of a punctured surface. If time permits, I will sketch an idea of the proof of our result and discuss a list of intriguing open questions.