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18.708

web Course website

Lectures on Operator Algebras

pdf Problem set (due: April 28) (updated: April 26)

Schedule:
  1. April 12. Hilbert spaces, projections, and physics
  2. April 14. Von Neumann algebras, states, and representations
  3. April 19. Subfactors and index
  4. April 21. The Temperley–Lieb algebra
References:
  • G. B. Folland. Quantum Field Theory: A Tourist Guide for Mathematicians. AMS Mathematical Surveys and Monographs, Vol. 149, AMS (2008).
  • C. K. Fan & R. M. Green. Monomials and Temperley–Lieb Algebras. J. Algebra, 190 (1997), 498-517.
  • V. F. R. Jones. Index for Subfactors. Invent. math., 72 (1983), 1-25.
  • V. F. R. Jones. A Polynomial Invariant for Knots via von Neumann Algebras. Bull. AMS, 12(1) (Jan. 1985), 103-111.
  • V. F. R. Jones. Hecke Algebra Representations of Braid Groups and Link Polynomials. Ann. of Math. (2), 126(2) (Sep., 1987), 335-388.
  • V. F. R. Jones. Von Neumann Algebras. Vanderbilt University. Unpublished notes (November 13, 2015).
  • D. Kazhdan & G. Lusztig. Representations of Coxeter Groups and Hecke Algebras. Invent. math., 53 (1979), 165-184.