NCMW Operator Algebras, Quantum Groups and Noncommutative Geometry (2019)

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Venue: IISER,  Bhopal, Madhya Pradesh
Date:  1st, Jul 2019 to 13th, Jul 2019

 

School Convener(s)

Name Dr. Prahlad Vaidyanathan Dr. Angshuman Bhattacharya Dr. Rohit Dilip Holkar
Mailing Address

Office 202, Academic Building 1,
IISER Bhopal, Bhopal ByPass Road,
Bhauri, Bhopal 462066.
Madhya Pradesh.

Office 201, Academic Building 1,
IISER Bhopal, Bhopal ByPass Road,
Bhauri, Bhopal 462066.
Madhya Pradesh.

Office 305, Academic Building 1,
IISER Bhopal, Bhopal ByPass Road,
Bhauri, Bhopal 462066.
Madhya Pradesh.

 


 Speakers with their affiliations:

Name of the speaker

Position

Affiliation / official postal address

Dr. Sutanu Roy

Assistant Professor

National Institute of Science Education and Research Bhubaneshwar

Dr. Sayan Chakraborty

Post-Doctoral Researcher

Indian Institute of Science Education and Research Bhopal

Prof. Arup Kumar Pal

Professor

Indian Statistical Institute, Delhi

Dr. Prahlad Vaidyanathan

Assistant Professor

Indian Institute of Science Education and Research Bhopal

Dr.Rohit Holkar

Assistant Professor

Indian Institute of Science Education and Research Bhopal

 List of Tutors

Name of the tutor

Position

Affiliation / official postal address

Ms. Anshu

PhD Scholar

IISER Bhopal

Ms. Apurva Seth

PhD Scholar

IISER Bhopal

Mr. Sagar Shinde

PhD Scholar

IISER Bhopal

 


 Syllabus:

Name of the Speaker

Detailed Syllabus

Dr. Sutanu Roy

  • Finite Groups to Finite Dimensional Hopf Algebras. Recapitulation of compact groups and representation theory.

  • Compact quantum groups (CQG): Definition and Examples

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

  • Representation theory of CQGs

  • Tannaka-Krein-Woronowicz duality

  • Representation Category of SUq(2)

Dr. Rohit Holkar

  • Homotopy classes of Unitaries

  • Equivalence of Projections

  • K_0 of a unital C*-algebra

  • K_0 of a non-unital C*-algebra

  • Half-Exactness and Split Exactness

Dr. Sayan Chakraborty

  • Twisted group algebras and Examples

  • Crossed products of C*-algebras

  • K-theory of noncommutative tori

  • Extensions related to free groups and Kadison-Kaplansky conjecture.

Prof. Arup Kumar Pal

  • Lie groups and Lie Algebras

  • Finite dimensional representations of sl(2,C)

  • q-deformations of sl(2,C)

  • Finite dimensional representations of Uq(SL(2,C))

  • Revision of Peter-Weyl theory

  • Structure of representation category of Uq(SL(2,C))

  • Drinfeld deformation

Dr. Prahlad Vaidyanathan

  • Example: The Cuntz Algebra

  • Example: The Irrational Rotation Algebra

  • Order structure on K_0(A)

  • Inductive limits

  • Finite Dimensional C*-algebras

  • Classification of AF-algebras. Higher K-groups.

 


Time-Table

Day

Date

Lecture 1
(9.30 – 11.00)

Tea

Lecture 2
(11.30 – 1.00)

Lunch
1.00-2.00

Lecture 3
(2.00 – 3.30)

Tea

Discussion/
Tutorial
(4.00 – 5.00)

Tea &
snacks

name of the speaker
(abbr)

name of the speaker
(abbr)
name of the speaker
(abbr)
name of the speaker
(abbr)

Mon

1/7/19

SC

 

RH

 

SR

 

A, AS, SS

 

Tues

2/7/19

SC

 

RH

 

SR

 

A, AS, SS

 

Wed

3/7/19

SC

 

RH

 

SR

 

A, AS, SS

 

Thu

4/7/19

SC

 

RH

 

SR

 

A, AS, SS

 

Fri

5/7/19

AKP

 

RH

 

SR

 

A, AS, SS

 

Sat

6/7/19

AKP

 

RH

 

SR

 

A, AS, SS

 

 

Mon

8/7/19

SR

 

PV

 

AKP

 

A, AS, SS

 

Tue

9/7/19

SR

 

PV

 

AKP

 

A, AS, SS

 

Wed

10/7/19

SR

 

PV

 

AKP

 

A, AS, SS

 

Thu

11/7/19

SR

 

PV

 

AKP

 

A, AS, SS

 

Fri

12/7/19

SR

 

PV

 

AKP

 

A, AS, SS

 

Sat

13/7/19

SR

 

PV

 

AKP

 

A, AS, SS

 

Full forms for the abbreviations of speakers and tutors :

  • SC : Sayan Chakraborty
  • RH : Rohit Holkar
  • SR : Sutanu Roy
  • AKP : Arup Kumar Pal
  • A : Anshu
  • AS : Apurva Seth
  • SS : Sagar Shinde
  • PV : Prahlad Vaidyanathan

List of actual Participants

Sr SID Full Name Gender Affiliation Position in College/ University University
/Institute M.Sc./ M.A.
Year of Passing M.Sc./ M.A Ph.D. Deg
Date
1   Dr. Sutanu Roy   NISER Bhubaneshwar Assistant Professor      
2   Prof. Arup Kumar Pal   ISI Delhi Professor      
3   Dr. Sayan Chakraborty   IISER Bhopal Post-Doc      
4   Dr. Rohit Holkar   IISER Bhopal Assistant Professor      
5   Dr. Prahlad Vaidyanathan   IISER Bhopal Assistant Professor      
6   Dr. Angshuman Bhattacharya   IISER Bhopal Assistant Professor      
7   Anshu   IISER Bhopal PhD Student      
8   Apurva Seth   IISER Bhopal PhD Student      
9   Sagar Shinde   IISER Bhopal PhD Student      
10 24717 Mr. Pankaj Dey Male IISER Thiruvananthapuram Integrated PHD IISER Thiruvananthapuram 2017  
11 24736 Mr. Mahesh Krishna K Male (NITK) Surathkal Research Scholar Mangalore University 2014  
12 25025 Mr. Sreejith Siju Male Indian Institute of Technology PhD Student CMS College Kottayam 2015  
13 25489 Dr Lavy Koilpitchai Male Indian Statistical Institute Visiting scientist Pondicherry University 2011 14/06/2018
14 25512 Mr Repana Devendra Male IIT Madras PhD University of Hyderabad 2014  
15 25701 Mr. Pappu Anuragi Male Ramanujan college University of Delhi Assistant Professor IIT Bombay 2010  
16 25892 Ms. Neeru Bala Female IIT, Hyderabad Ph.D student University Of Delhi 2015  
17 26182 Mr. Azad Rohilla Male THE LNM Institue of Information Technology PhD University of Delhi 2017  
18 26236 Mr. Dimple Male The LNM Institute of Information Technology Ph.D University of Delhi 2017  
19 26629 Ms Rachna Aggarwal Female University of Delhi PhD University of Delhi 2011  
20 26926 Mr. Manish Kumar Male Indian Statistical Institute, Bangalore PhD Indian Institute of Science 2016  
21 27142 Mr. Amit Kumar Male NISER Bhubaneswar PhD IIT Guwahati 2014 26/03/2019
22 27540 Mr. Atibur Rahaman Male NISER PhD Jadavpur University 2015  
23 27669 Mr. Bharat Talwar Male University o Delhi Ph.D. Student University of Delhi 2016  
24 27996 Mr. Shubham Rameshsingh Bais Male Indian Institute of Technology Hyderabad Ph. D. Pondicherry University 2017  
25 28001 Ms. Shanola Smitha Sequeira Female IIT Hyderabad Ph. D. Pondicherry University 2017  
26 28080 Mr. Debabrata Jana Male IIT Kanpur PhD Bananas Hindu University 2017  
27 28228 Mr. Arindam Ghosh Male Indian Institute of Technology, Hyderabad PhD Presidency University 2017  
28 28230 Mr. Anindya Ghatak Male ISI Bangalaru Visitting Scientist Calcutta Univeristy 2012 16/04/2019
29 28286 Ms. Piyasa Sarkar Female Institute of Mathematical Sciences PhD Indian Institute of Technology, Kanpur 2017  
30 28429 Mr. Chaitanya Janardan Kulkarni Male IISER Bhopal PhD Department of Mathematics Savitribai Phule Pune University 2012  
31 28443 Mrs Md Amir Hossain Male IISER Bhopal PhD West Bengal State University. 2015  

 


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