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Lecture Video

SES # Date Title Video
1 Jun. 11, 2015
Introduction to von Neumann algebras. Definition and examples. Von Neumann density theorem. Factors of types I,II and III. Tomita-Takesaki theory and Connes decomposition and classification. Hyperfiniteness. Video
2 Jun. 12, 2015
Subfactors and elementary examples. Index in the type II case. Bimodules. The tower of relative commutants and restrictions on index values. Construction of examples. Braid group representations and knot polynomials. Video
3 Jun. 15, 2015
Kauffman diagrams for the Temperley-Lieb algebra. Planar algebras, lambda lattices - the standard invariant of a subfactor and reconstruction. Random matrices with a real number of matrices. Tensor categories, 2-categories. Endomorphisms and the type III approach. Video
4 Jun. 17, 2015
Classification of small index subfactors. Izumi’s Cuntz algebra approach. Skein theory presentations of subfactors, the exchange relation, the Yang-Baxter equation and the jellyfish algorithm. Video
5 Jun. 19, 2015
Algebraic quantum field theory, conformal field theory and scaling limits of statistical mechanical models. Hilbert spaces from planar algebras-a toy algebraic QFT and the Thompson groups. Knots and links from the Thompson groups. Video