ATMW Operator Algebra (2017)

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Venue: The Institute of Mathematical Sciences,  Chennai, Tamil Nadu
Date:  11th, Sep 2017 to 16th, Sep 2017

 


 

School Convener(s)

Name Prof. Vijay Kodiyalam Prof. Partha Sarathi Chakraborty
Mailing Address Department of Mathematics
The Institute of Mathematical Sciences (IMSc)
IV Cross Road, CIT Campus, Taramani
Chennai, Tamil Nadu – 600113
Department of Mathematics
The Institute of Mathematical Sciences (IMSc)
IV Cross Road, CIT Campus, Taramani
Chennai, Tamil Nadu – 600113

 


 

Speakers and Syllabus 

 Speakers and their affiliations with detailes of lecture

Speakers Details of lectures delivered
Prof. Partha Sarathi Chakraborty
IMSc
Lectures 1,2: Fredholm operators, Atkinson's Theorem, additivity of indexunder composition, invariance of the index under norm small perturbations,continuity of the index map.
Lectures 3,4: Basics of Hilbert C*-modules and adjointable operators,polar decomposition.
Lectures 5,6: Finitely generated submodules of ${\mathcalH}_A$,Generalized Fredholm operators, Generalized Atkinson's theorem,well-definedness of index.
 Prof. Sundar Sobers
 CMI
Lecture 1: C*-algebras, projections, partial isometries, Grothendieckconstruction, Definition of K_0, homotopy invariance ofK_0.
Lecture 2: Half exactness and split exactness of K_0, stability of K_0,Definition of K_1, homotopy invariance of K_1, halfexactnessof K_1
Lecture 3 : Split exactness of K_1, stability of K_1, Index map, K-theoryof the suspension of a C*-algebra, the isomorphism K_1(A) \cong K_0(SA), quasi-homomorphisms and its properties.
Lecture 4: Shift operator, Toeplitz C*-algebra, the standard exact sequenceof the Toeplitz algebra, Coburn's theorem, Wolddecomposition ofan isometry.
Lecture 5 : Proof of Bott periodicity i.e. K_0(A) \cong K_1(SA), six termsequence, examples, Hilbert C*-modules, adjointable operators,compact operators.
Lecture 6 : Internal tensor product of Hilbert C*-modules, statement ofPimsner-Voiculescu sequence, Toeplitz extension of the crossed product by Z, sketch of the proof of PV sequence.
Prof. Kunal Krishna Mukherjee,
IITM
left and right Hilbert algebras, deduced several properties or auxiliary results to deal with left and right multiplication operators, considered  full left andright Hilbert algebras,and showed that left and the right vonNeumann algebras associated to theconstructions are commutants of each other. In the last talk,  sketched the structure theory of type III factors and somefacts about KMS condition.

 


 
Time Table

Day

Date

Lecture 1

(9.30
to
11.00)

Tea

(11.05
to
11.25)

Lecture 2

(11.30
to
1.00)

Lunch

(1.00
to
2.00)

Lecture 3

(2.00
to
3.30)

Tea

(3.35
to
3.55)

Discussion

(4.00
to
5.00)

Snacks
5.05
to
  5.35      

 

 

(speaker)

 

(speaker))

 

(speaker)

 

(speaker /tutor)

 

Mon

11.09.2017

PC

 

KM

 

SS

 

PC

 

Tue

12.09.2017

PC

 

KM

 

SS

 

DD

 

Wed

13.09.2017

KM

 

SS

 

PC

 

SS

 

Thu

14.09.2017

PC

 

KM

 

SS

 

PC

 

Fri

15.09.2017

KM

 

PC

 

SS

 

DD

 

Sat

16.09.2017

PC

 

KM

 

SS

 

PC

 

PC: Partha Sarathi Chakraborty
KM: Kunal Mukherjee
SS: Sundar Sobers
DD: Debabrata De


 

Actual Participants 
Sr.n SID Full Name Gender Affiliation Position in College/ University University/Institute M.Sc./ M.A. Year of Passing M.Sc. / M.A Ph.D. Degree Date
1 13419 Mr. Pappu Anuragi Male Ramanujan College(University of Delhi) Asst. Professor IIT Bombay 2010  
2 13428 Ms. Kubra Nazera A R Female Anna university, Chennai Research scholar - Ph.D Anna university, Chennai, M.Sc 2012  
3 13436 Mr. Mahesh Krishna K Male NIT Karnataka Surathkal Ph.D. Student Mangalore University 2014  
4 13453 Mr. Animesh Bhandari Male NIIT Meghalaya PhD Student Ramakrishna Mission Vidyamandira 2010  
5 13477 Mr Veera Mani Male IIT Hyderabad PhD MSc 2010  
6 13496 Ms Aisha Jabeen Female Aligarh Muslim University phd student Aligarh Muslim University 2011  
7 13540 Ms. Swati Setia Female Harish-Chandra Research Institute Project Assistant Thapar University 2016  
8 13594 Mr. Bilal Ahmad Wani Male Aligarh Muslim University PhD University of Kashmir 2012  
9 13939 Ms. Neeru Bala Female Indian Institute Of Technology Ph.D University Of Delhi 2015  
10 14015 Mr. Siddharth Ganesh Shete Male M.B. College Latur Ph. D. Student S.R.T.M.U. Nanded 2014  
11 14169 Mr. Adnan Abbasi Male Aligarh Muslim University PhD Scholar Jamia Millia Islamia 2012  
12 14171 Mr. Nazim Khan Male Aligarh Muslim University PhD Scholar Aligarh Muslim University 2015  
13 14354 Ms. Anshu Nirbhay Female Indian Institute of Science Education and Research Bhopal Integrated PhD Student IISER Bhopal 2016  
14 14410 Mr Kiran Virivinti Male University College of Engineering Assistant Professor osmania 2002 5/31/2016
15 14446 Mr. Purbayan Chakraborty Male Presidency University, Kolkata M.Sc. final year student Presidency University    
16 - Mumtaz Fathima   MIT Chromepet        
17   Soumen Roy   IIT Madras        
18   Debabrata De   IIT Madras        
19   Rahul Kumar   IIT Madras        
20   Lavy Koilpitchai   IIT Madras        
21   Pradyot Karmakar   IIT Madras        
22   Bipul Saurabh   IMSc Chennai        
23   Vijay Kodiyalam   IMSc Chennai        
24   Partha Sarathi Chakraborty   IMSc Chennai        
25   Kunal Krishna Mukherjee   IIT Madras        
26   Sundar Sobers   CMI Chennai        

 

 


How to reach

The Chennai neé Madras, and to IMSc, the Institute of Mathematical Sciences. Here is some information on getting to the Institute. Address and phone numbers are

THE INSTITUTE OF MATHEMATICAL SCIENCES
C I T CAMPUS, TARAMANI, CHENNAI 600 113
Telephone Numbers

Here are some maps to give you a rough idea of the layout of Madras and the area around the Institute.

The Institute of Mathematical Sciences is located in a campus-like area variously known as the ``CIT Campus'' or the ``CPT Campus''. Many people in Madras may not have heard of the Institute, but almost everyone would have heard of the M.G.R. Film City and Tidel Park which are further down in the same campus area. IMSc has two complexes. One houses the main Institute building, the library building and the new building. The other has the students' hostel and Guest House. These two complexes are across the road from each other.