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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 18th 2013
   • (edited Dec 18th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYou may remember that I had announced the following thesis to appear a while back in the context of _[[extended geometric quantization of 2d Chern-Simons theory]]_; now it is in the last finalization stages: * Stephan Bongers, _Geometric quantization of symplectic and Poisson manifolds_ master thesis, Utrecht 2013 (**[pdf](https://dl.dropboxusercontent.com/u/12630719/ThesisBongers2013.pdf)**, **[web](http://ncatlab.org/schreiber/show/master+thesis+Bongers)**) **Abstract.** The first part of this thesis provides an introduction to recent developments in geometric quantization of symplectic and Poisson manifolds, including modern refinements involving Lie groupoid theory and index theory/K-theory. We start by giving a detailed treatment of traditional geometric quantization of symplectic manifolds, where we cover both the quantization scheme via polarization and via push-forward in K-theory. A different approach is needed for more general Poisson manifolds, which we treat by the geometric quantization of Poisson manifolds via the geometric quantization of their associated symplectic groupoids, due to Weinstein, Xu, Hawkins, et al. In the second part of the thesis we show that this geometric quantization via symplectic groupoids can naturally be understood as an instance of higher geometric quantization in higher geometry, namely as the boundary theory of the 2d Poisson sigma-model. This thesis closes with an outlook on the implications of this change of perspective.

   You may remember that I had announced the following thesis to appear a while back in the context of extended geometric quantization of 2d Chern-Simons theory; now it is in the last finalization stages:

   • Stephan Bongers,

     Geometric quantization of symplectic and Poisson manifolds

     master thesis, Utrecht 2013

     (pdf, web)

   Abstract. The first part of this thesis provides an introduction to recent developments in geometric quantization of symplectic and Poisson manifolds, including modern refinements involving Lie groupoid theory and index theory/K-theory. We start by giving a detailed treatment of traditional geometric quantization of symplectic manifolds, where we cover both the quantization scheme via polarization and via push-forward in K-theory. A different approach is needed for more general Poisson manifolds, which we treat by the geometric quantization of Poisson manifolds via the geometric quantization of their associated symplectic groupoids, due to Weinstein, Xu, Hawkins, et al. In the second part of the thesis we show that this geometric quantization via symplectic groupoids can naturally be understood as an instance of higher geometric quantization in higher geometry, namely as the boundary theory of the 2d Poisson sigma-model. This thesis closes with an outlook on the implications of this change of perspective.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 26th 2014
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   Author: Urs
   Format: MarkdownItexThe defense of the thesis is tomorrow. At _[[schreiber:master thesis Bongers]]_ there are now his talk slides and some more pointers as to what is going on in the thesis.

   The defense of the thesis is tomorrow. At master thesis Bongers (schreiber) there are now his talk slides and some more pointers as to what is going on in the thesis.