{"id":265,"date":"2023-11-09T11:31:49","date_gmt":"2023-11-09T11:31:49","guid":{"rendered":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=265"},"modified":"2023-11-09T11:31:49","modified_gmt":"2023-11-09T11:31:49","slug":"geometry-and-representation-theory","status":"publish","type":"page","link":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=265","title":{"rendered":"Geometry and Representation\u00a0Theory"},"content":{"rendered":"\n

Working Seminar Winter 2015<\/a><\/h1>\n\n\n\n

The topic of the seminar is the WZW model in conformal field theory, focusing on geometrical aspects – in particular the construction of the (flat projective) WZW on the bundles over the moduli space of stable curves . One could describe this as \u201ca gift of representation theory to geometry, prophesied by physics\u201d. In the first half of the seminar we will focus on the (infinite-dimensional) representation theory that is needed, and then we will use this to tell the (finite-dimensional) geometric story. At the end we will discuss some of the physics behind this, and possibly give some recent applications in topology or geometry.<\/p>\n\n\n\n

The seminar will meet weekly on Tuesdays from 5 till 6 pm in JCMB 5326, during S2 of 2014-15. In the first meeting we will give an introduction, and divide the work for the rest of the seminar.<\/p>\n\n\n\n

Seminar schedule:<\/a><\/h2>\n\n\n\n
Date<\/td>Topic<\/td>Speaker<\/td><\/tr>
<\/td><\/td><\/td><\/tr>
20 Jan<\/td>Introduction & organization of the seminar. Quick review of highest-weight representations of semi-simple Lie algebras.<\/td>Johan Martens<\/td><\/tr>
27 Jan<\/td>Introduction to affine Kac-Moody algebras.\u00a0Noah’s notes<\/a>.<\/td>Noah White<\/td><\/tr>
3 Feb<\/td>Representation theory of affine Lie algebras.<\/td>David Jordan<\/td><\/tr>
10 Feb<\/td>The Virasoro algebra and its representations. Segal-Sugawara construction.<\/td>Sue Sierra<\/td><\/tr>
17 Feb<\/td>No seminar<\/td><\/td><\/tr>
24 Feb<\/td>Generalities on (projective) connections, Atiyah algebroids, twisted D-modules.<\/td>Chunyi Li<\/td><\/tr>
3 Mar<\/td>Brief intro to stacks, M_g,n-bar and the Hodge bundle.<\/td>Sjoerd Beentjes<\/td><\/tr>
10 Mar<\/td>Construction of WZW conformal blocks bundles. Factorization.<\/td>Salvatore Dolce<\/td><\/tr>
17 Mar<\/td>Fusion Rules and the Verlinde Formula.<\/td>Salvatore Dolce<\/td><\/tr>
24 Mar (4-6pm)<\/td>The WZW flat projective connection.<\/td>Johan Martens<\/td><\/tr>
31 Mar<\/td>The WZW model in conformal field theory.<\/td>Jos\u00e9 Figueroa-O’Farrill<\/td><\/tr>
7 Apr (4-5pm)<\/td>The WZW model in conformal field theory continued.<\/td>Jos\u00e9 Figueroa-O’Farrill<\/td><\/tr>
7 Apr (5-6pm)<\/td>WZW model and modular functors.<\/td>Adrien Brochier<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Some relevant literature & other resources:<\/a><\/h2>\n\n\n\n