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QS - Seminar: K-theory for operator algebras, categorification and higher twists February 27, 2020 (02:00 PM PST - 04:30 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) David Evans (Cardiff University)
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This talk is  part of a programme to understand conformal field theory through K-theory, in particular twisted equivariant K-theory.

I describe work with Andreas Aaserud on the actions of braided C*-tensor categories on operator algebras or realizing these categories as modules over an operator algebra. Freed Hopkins Teleman realized  the Verlinde ring of positive energy representations of loop groups through twisted equivariant K-theory of the section algebra of equivariant bundles of compact operators. In work with Ulrich Pennig, we prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (ie. non-classical) twist of K-theory over G=SU(n), employing the section algebra of a locally trivial bundle with stabilised strongly self-absorbing fibres.

Using a version of the Mayer-Vietoris spectral sequence we compute the equivariant higher twisted K-groups for arbitrary exponential functor twists over SU(2), and also over SU(3) after rationalisation.

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