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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Tutte's golden identity from a fusion category

## Tutte's golden identity from a fusion categoryAdd to your list(s) Download to your calendar using vCal - Paul Fendley (University of Oxford)
- Tuesday 14 March 2017, 14:00-15:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. OAS - Operator algebras: subfactors and their applications The chromatic polynomial \chi(Q) can be defined on any graph, such that for Q integer it counts the number of colourings. In statistical mechanics, it is known as the partition function of the antiferromagnetic Potts model on that graph. It has many remarkable properties, and Tutte's golden identity is one of the more unusual ones. For any planar triangulation, it relates \chi(\phi+2) to the square of \chi(\phi+1), where \phi is the golden mean. Tutte's original proof is purely combinatorial. I will give here an elementary proof using fusion categories, which are familiar for example from topological quantum field theory, anyonic quantum mechanics, and integrable statistical mechanics. In this setup, the golden identity follows by simple manipulations of a topological invariant related to the Jones polynomial. I will also mention recent work by Agol and Krushkal on understanding what happens to the identity for graphs on more general surfaces. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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