Prof. Gennadi Kasparov SGU Special Lecture (Introduction to Index theory and KKtheory)
SGU Special lectures by Prof. Gennadi Kasparov will take place as follows:
 Date & Time
 13:0015:00 on every Wednesday starting on October 17 until Novenber 28.
 Venue
 October 24 & November 14: 305, other days: 108, Faculty of Science Bldg. #3, Kyoto University
 Title
 Introduction to Index theory and KKtheory
 Abstract
 The course will contain the operator Ktheory approach to the AtiyahSinger index theorem. We will start with some classical examples of elliptic differential operators on compact smooth manifolds without boundary. This will naturally lead us to two special cases of KKtheory: Kcohomology and Khomology.
KKtheory will be introduced gradually, as much as it is needed for index theory. Most examples will come from differential and pseudodifferential operators. Large part of technical results related with $KK$theory will be given without proof: because time is limited, and also because we need $KK$theory for this course only as a tool.
Other technical tools include Clifford algebras and Dirac operators. Although all definitions will be given in the course, I advise the listeners to consult the book ``Spin geometry'' by H. B. Lawson and M.L. Michelsohn on these issues.
The main part of the course will contain a proof of the $K$theoretic version of the AtiyahSinger index theorem. The cohomological AtiyahSinger index formula for compact manifolds will be obtained as a corollary. Various applications will be discussed as much as time allows.

Recommended literature:
1. M. F. Atiyah, I. M. Singer: ``The index of elliptic operators'', I, III, Annals of Math., 87 (1968), 484530, 546604.
2. H. B. Lawson, M.L. Michelsohn: ``Spin geometry'', Princeton Univ. Press, 1989.
 Language
 English