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, Pseudo-differential operators on torus and elliptic problems, Kadison-Kaplansky 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

K-theory: Homotopy classes of projections and unitaries, K_0 group of unital and non-unital C*-algebras, Examples.

Dr. Prahlad Vaidyanathan, IISER Bhopal (PV)

6 lectures of 1.5 hour each = 9 hours.

K-theory: 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, Tannaka-Krein-Woronowicz duality, Representation category of SUq(2)

 References:

Books:

  • M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag (2001).
  • P.B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, CRC Press (2018).
  • A. Connes, Noncommutative Geometry, Academic Press (1994).
  • M. Rordam, F. Larsen, and N. Laustsen, An Introduction to K-theory for C*-algebras, Cambridge University Press (2000)
  • N.E. Wegge-Olsen, K-theory 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. 41-144.

Time Table

Names of Tutors with their affiliation:

  1. Ms. Anshu (IISER Bhopal)
  2. Ms. Apurva Seth (IISER Bhopal)
  3. Mr. Sagar Shinde (IISER Bhopal)

Tentative timetable with names of speakers and their affiliations:

 

Day

Date

Lecture 1:
9.30-11.00

Tea

Lecture 2:
11.30-1.00

Lunch

Lecture 3:
2.00-3.30

Tea

Tutorial:
4.00-5.00

Mon

01-07-19

(PC)
Fredholm Theory

 

 

 

 

 

 

(RH) Homotopy Classes of Unitaries

 

 

 

 

 

 

(SR)
Finite groups to finite dimensional Hopf-algebras

 

 

 

 

 

 

Noncommutative Geometry Tutorial

Tue

02-07-19

(PC)
Fredholm Theory

(RH) Equivalence of Projections

(SR) Recapitulation of compact groups and representation theory

K-theory Tutorial

Wed

03-07-19

(PC)
Pseudo differential operators on torus and elliptic problems.

(RH)
K_0 of a unital C*-algebra

(SR)
Compact quantum groups (CQG): Definition and Examples

Quantum Groups Tutorial

Thu

04-07-19

(PC)
Pseudo differential operators on torus and elliptic problems.

(RH)
K_0 of a unital C*-algebra

(SR)
Compact quantum groups (CQG): Existence of Haar state

Noncommutative Geometry Tutorial

Fri

05-07-19

(PC)
Pseudo differential operators on torus and elliptic problems.

(RH)
K_0 of a non-unital C*-algebra

(SR) Representation theory of CQGs-1

K-theory Tutorial

Sat

06-07-19

(PC)
Kadison-Kaplansky conjecture for free group on two generators

(RH)
Half-Exactness and Split Exactness

(SR) Representation theory of CQGs-2

Quantum Groups Tutorial

Sun

07-07-19

Break

Mon

08-07-19

(SR) Representation theory of CQGs-3

 

 

 

 

 

 

(PV)
K_1 of a C*-algebra

 

 

 

 

 

 

(PC)
Cyclic cohomology

 

 

 

 

 

 

Noncommutative Geometry Tutorial

Tue

09-07-19

(SR) Representation theory of CQGs-4

(PV) Functoriality and Exactness of K_1

(PC)
Cyclic cohomology

K-theory Tutorial

Wed

10-07-19

(SR)
Tannaka-Krein-Woronowicz duality-1

(PV) Definition of Index Map

(PC)
Fredholm Cycles and Index Pairing

Quantum Groups Tutorial

Thu

11-07-19

(SR)
Tannaka-Krein-Woronowicz duality-2

(PV)
Long Exact sequence in K-theory

(PC)
Fredholm Cycles and Index Pairing

Noncommutative Geometry Tutorial

Fri

12-07-19

(SR)
Tannaka-Krein-Woronowicz duality-3

(PV)
Bott periodicity

(PC)
The case of compact quantum groups

K-theory Tutorial

Sat

13-07-19

(SR) Representation Category of SUq(2)

(PV)
Six term exact sequence

(PC)
The case of compact quantum groups

Quantum Groups Tutorial

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