Lecture Notes

  • Slides of my series of lectures on “Introduction to Noncommutative Geometry” at UC Berkeley in Spring 2015. (Many thanks to Prof. Marc Rieffel for letting me give these lectures in his Quantum Geometry seminar.)
    • Part 1: Quantized Calculus (pdf).
    • Part 2: Spectral Triples (pdf).
    • Part 3: Cyclic Homology and Cohomology (pdf).
    • Part 4: Index Theory and the Connes-Chern Character (pdf).

  • Slides of my short courses on noncommutative geometry at Yau Mathematical Science Center, Tsinghua University, Beijing, China (October 24–27, 2011) and Australian National University, Canberra, Australia (August 2012).
    • Part 1: Introduction (Quantized Calculus) (pdf).
    • Part 2: Spectral Triples and the Atiyah-Singer Index Theorem (pdf).
    • Part 3: Cyclic Cohomology (pdf).
    • Part 4: The Local Index Formula in Noncommutative Geometry (pdf).
    • Part 5: Diffeomorphism-Invariant Geometry (pdf).

  • Notes of my graduate courses on noncommutative geometry at the University of Tokyo (Oct. 2010 – Jan. 2011) and Seoul National University (Spring 2012 and Spring 2018).
    • Chap. 1-7: Operator ideals, Connes’ quantized calculus, Dixmier trace, pseudodifferential operators, the noncommutative residue, lower dimensional volumes in Riemannian geometry (pdf).
    • Chap. 8.: Clifford algebras, spinors, Dirac operators and the Atiyah-Singer index theorem (pdf).
    • Chap. 9-12: K-theory, cyclic cohomology, the local index formula in NCG, the CM cocycle for Dirac spectral triples, Connes-Moscovici’s index theorem in diffeomorphism-invariant geometry (pdf).