Vaughan F. R. Jones教授（京都大学 / Vanderbilt University）による京都大学SGU特別講義を下記の要領で行います。

科目名

SGU数学特別講義（作用素環論）

日　時

2015年6月11日〜6月19日
6月11日(木)　10:00〜12:00
6月12日(金)　10:00〜12:00
6月15日(月)　15:00〜17:00
6月17日(水)　10:00〜12:00
6月19日(金)　10:00〜12:00

場　所

京都大学理学部３号館 127大会議室

題　目

An Introduction to Subfactors in Mathematics and Physics

概　要

We intend to describe the current state of classification of subfactors and attack the question of whether all subfactors have something to do with quantum field theory, including an appearance of Richard Thompson's groups F and T.

Lecture 1. 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.

Lecture 2. 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.

Lecture 3. 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.

Lecture 4. 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.

Lecture 5. 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.

言　語

英語