NCMW  Operator Algebras, Quantum Groups and Noncommutative Geometry (2019)
Speakers and Syllabus
Name of the Speaker with Affiliation 
No. Of Lectures 
Detailed Syllabus 
Outstation Speakers 


Dr. Partha Sarathi Chakraborty, ISI Kolkata (PC) 
12 lectures of 1.5 hours each = 18 hours. 
Noncommutative Geometry: Fredholm theory, Pseudodifferential operators on torus and elliptic problems, KadisonKaplansky conjecture for free group on two generators, cyclic cohomology,Fredholm Cycles and Index Pairing, The case of compact quantum groups 
Dr. Rohit Dilip Holkar, IISER Bhopal (RH) 
6 lectures of 1.5 hours each = 9 hours 
Ktheory: Homotopy classes of projections and unitaries, K_0 group of unital and nonunital C*algebras, Examples. 
Dr. Prahlad Vaidyanathan, IISER Bhopal (PV) 
6 lectures of 1.5 hour each = 9 hours. 
Ktheory: K_1 group of a C*algebra, Index Map, Bott periodicity, Six term exact sequence 
Dr. Sutanu Roy, NISER Bhubaneshwar (SR) 
12 lectures of 1.5 hours each = 18 hours. 
Compact Quantum Groups: Finite groups to finite dimensional Hopf algebras, Compact groups and their representation theory, Definition and examples of Compact Quantum groups, Existence of Haar states, Representation theory, TannakaKreinWoronowicz duality, Representation category of SUq(2) 
References:
Books:
 M. A. Shubin, Pseudodifferential Operators and Spectral Theory, SpringerVerlag (2001).
 P.B. Gilkey, Invariance Theory, the Heat Equation, and the AtiyahSinger Index Theorem, CRC Press (2018).
 A. Connes, Noncommutative Geometry, Academic Press (1994).
 M. Rordam, F. Larsen, and N. Laustsen, An Introduction to Ktheory for C*algebras, Cambridge University Press (2000)
 N.E. WeggeOlsen, Ktheory and C*algebras: A Friendly Approach, Oxford University Press (1994)
 S. Neshveyev and L. Tuset, Compact Quantum Groups and their Representation Categories, American Mathematical Society (2013).
 T. Timmerman, An Invitation to Quantum Groups and Duality, European Mathematical Society (2008).
Articles:
 V. Guillemin, Lectures on Spectral Theory of Elliptic Operators, Duke Math J. 44 (1977) No. 3.
 A. Connes, Noncommutative Differential Geometry, Publications Mathematique de l’IHES Vol. 62 (1985), p. 41144.
Time Table
Names of Tutors with their affiliation:
 Ms. Anshu (IISER Bhopal)
 Ms. Apurva Seth (IISER Bhopal)
 Mr. Sagar Shinde (IISER Bhopal)
Tentative timetable with names of speakers and their affiliations:
Day 
Date 
Lecture 1: 
Tea 
Lecture 2: 
Lunch 
Lecture 3: 
Tea 
Tutorial: 
Mon 
010719 
(PC) 

(RH) Homotopy Classes of Unitaries 

(SR) 

Noncommutative Geometry Tutorial 
Tue 
020719 
(PC) 
(RH) Equivalence of Projections 
(SR) Recapitulation of compact groups and representation theory 
Ktheory Tutorial 

Wed 
030719 
(PC) 
(RH) 
(SR) 
Quantum Groups Tutorial 

Thu 
040719 
(PC) 
(RH) 
(SR) 
Noncommutative Geometry Tutorial 

Fri 
050719 
(PC) 
(RH) 
(SR) Representation theory of CQGs1 
Ktheory Tutorial 

Sat 
060719 
(PC) 
(RH) 
(SR) Representation theory of CQGs2 
Quantum Groups Tutorial 

Sun 
070719 
Break 

Mon 
080719 
(SR) Representation theory of CQGs3 

(PV) 

(PC) 

Noncommutative Geometry Tutorial 
Tue 
090719 
(SR) Representation theory of CQGs4 
(PV) Functoriality and Exactness of K_1 
(PC) 
Ktheory Tutorial 

Wed 
100719 
(SR) 
(PV) Definition of Index Map 
(PC) 
Quantum Groups Tutorial 

Thu 
110719 
(SR) 
(PV) 
(PC) 
Noncommutative Geometry Tutorial 

Fri 
120719 
(SR) 
(PV) 
(PC) 
Ktheory Tutorial 

Sat 
130719 
(SR) Representation Category of SUq(2) 
(PV) 
(PC) 
Quantum Groups Tutorial 