Seoul National University

Introduction to Noncommutative Geometry
(a.k.a. Operator Algebras)
Spring 2012

Prof. Raphaël Ponge

Time and Location:

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Course Outline:


Main References:

  1. Connes, A.: Noncommutative geometry. Academic Press, San Diego, 1994. (Available online here.)

  2. Connes, A.; Moscovici, H.: The local index formula in noncommutative geometry. Geometric and Functional Analysis 5 (1995), 174-243. (Available online here.)

  3. Connes, A.; Moscovici, H.: Hopf algebras, cyclic cohomology and the transverse index theorem. Communications in Mathematical Physics 198 (1998), 199--246. (Available online here.)

  4. Gracia-Bondía, J.M.; Várilly, J.C.; Figueroa, H.: Elements of Noncommutative Geometry. Birkhäuser, Boston, 2001.

  5. Higson, N.: The residue index theorem of Connes and Moscovici. Surveys in Noncommutative Geometry, 71-126, Clay Mathematics Proceedings 6, AMS, Providence, 2006. (Available online here.)

  6. Ponge, R.: Noncommutative geometry and lower dimensional volumes in Riemannian geometry. Letters in Mathematical Physics 83 (2008) 19-32. (Available online here.)

  7. Ponge, R.: Introduction to Noncommutative Geometry. Lecture notes, graduate course, University of Tokyo, Oct. 2010-Jan. 2011 (Available online here.)

  8. Skandalis, G.: Noncommutative geometry, the transverse signature operator, and Hopf algebras (translated from French by R. Ponge and N. Wright). Operator algebras and noncommutative geometry II, Encyclopaedia of Mathematical Sciences, 121, pp. 115-134. Springer Verlag, Berlin, 2004.