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September 1, 2009

Ben-Zvi’s Lectures on Topological Field Theory III

Posted by Alexander Hoffnung

together with Orit Davidovich

The following is the third set of notes following the talks of David Ben-Zvi at a workshop on topological field theories, held at Northwestern University in May 2009. This post follows our second post found here. We’ll again give a brief introduction, and then send you over to a PDF file for the full set of notes.

The first lecture considered an example of a 22-dimensional TFT constructed from a finite group Γ\Gamma by assigning to the point the category of modules of the group algebra [Γ]\mathbb{C}[\Gamma]. The second lecture covered categorical versions of the group algebra for a complex reductive group GG. This was in preparation for a discussion of topological field theories associated to GG. These require higher categorical constructions, namely, 22-categories of GG-module categories assigned to the point.

This lecture focuses on two versions of GG-module categories: algebraic GG-categories and smooth GG-categories. By a result of Ben-Zvi, Francis and Nadler, assigning the 22-category of algebraic GG-categories to the point defines a 22-dimensional TFT. Assigning the 22-category of smooth GG-categories to the point only defines a 11-dimensional TFT. A modified version extends up to 22-manifolds. This modification is defined by assigning to the point the 22-category of \mathcal{H}-mod where \mathcal{H} is the finite Hecke category. From a physics perspective all of these are part of a 33-dimensional gauge theory.

Continue reading about lecture 3 here.

Posted at September 1, 2009 4:53 AM UTC

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Re: Ben-Zvi’s Lectures on Topological Field Theory III

Does “block matrices” on p4 mean “block diagonal matrices”?

Posted by: Allen Knutson on September 2, 2009 1:51 AM | Permalink | Reply to this

Re: Ben-Zvi’s Lectures on Topological Field Theory III

Yes, thanks Allen. It should say block-diagonal square matrices.

Posted by: Alex Hoffnung on September 2, 2009 7:03 AM | Permalink | Reply to this

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