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Lie Groups Quantum Mathematics Seminar

Modules over factorization spaces, and moduli spaces of parabolic G-bundles

Emily Cliff, University of Illinois Urbana-Champaign

Location:  Hill 705
Date & time: Friday, 16 February 2018 at 12:00PM - 1:20PM

Abstract:  Beilinson and Drinfeld introduced the notion of factorization algebras, a geometric incarnation of the notion of a vertex algebra. An advantage of working with factorization algebras is that they admit non-linear analogues, called factorization spaces, which can be viewed as both generalizations of and ways to produce examples of factorization algebras from algebraic geometry. The resulting factorization algebras can then be studied via the geometry of the spaces from which they arise. 

 Just as vertex algebras admit interesting categories of representations, so too do factorization algebras and factorization spaces. In this talk we will review the definitions of a factorization algebra and factorization space before introducing the notion of a module over a factorization space. As an example and an application we will construct moduli spaces of principal G-bundles with parabolic structures, and discuss how they can be linearized to recover modules over the factorization algebra corresponding to the affine Lie algebra associated to a reductive group G. The spaces we construct can be considered to form a "modular functor valued in spaces", which we linearize at different levels to recover the well-known WZW modular functors (valued in vector spaces). 


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