This workshop is intended for senior graduate students working in functional analysis with exposure to the subject as covered in the NCM AIS held at IMSc in Feb. 2015. Three main topics are scheduled to be covered

(1) Index of B-Fredholm operators and the Mischenko-Fomenko theorem

(2) Bottperiodicity and the Pimsner-Voiculescu exact sequence and

(3) Standard forms of von Neumann algebras.

**Syllabus to be covered in terms of modules of 6 lectures each :**

Name of the Speakers with affiliation. |
No. of Lectures |
Detailed Syllabus |

Partha Sarathi Chakraborty IMSc, Chennai | 6 | Fredholm and B-Fredholm operators and their index, Mischenko- Fomenko theorem. |

Sundar Sobers CMI, Chennai | 6 | Quasi-homomorphisms, Cuntz proof of Bott periodicity, Coburn's theorem, Wold decomposition, Crossed products by Z and Pimsner-Voiculescu exact sequence. |

Kunal Mukherjee IIT, Madras | 6 | Standard forms of von Neumann algebras upto Connes’ cocycle derivative. |

References:

1. K-theory and C*-algebras by Wegge-Olsen, papers of Mischenko-Foemnko

2. Topological and Bivariant K-theory by Cuntz, Meyer and Rosenberg.

3. Lectures on von Neumann algebras by Stratila.

(Lecture notes from the speakers, if available)

Tentative time-table with names of the speakers and tutors with their affiliation:

Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05–11.25) |
Lecture 2 (11.30–1.00) |
Lunch (1.00–2.00) |
Lecture 3 (2.00–3.30) |
Tea (3.35-3.55) |
Discussion (4.00-5.00) |
Snacks 5.05-5.35 |

(name of the speaker) | (name of the speaker) | (name of the speaker) | (Name of the speaker/tutor) | ||||||

Mon | 11.09.2017 | PC | KM | SS | TBA | ||||

Tue | 12.09.2017 | PC | KM | SS | TBA | ||||

Wed | 13.09.2017 | KM | SS | PC | TBA | ||||

Thu | 14.09.2017 | KM | SS | PC | TBA | ||||

Fri | 15.09.2017 | SS | PC | KM | TBA | ||||

Sat | 16.09.2017 | SS | PC | KM | TBA |