ATMW Operator Algebra (2017)
Venue:  The Institute of Mathematical Sciences, Chennai, Tamil Nadu 
Date:  11th, Sep 2017 to 16th, Sep 2017 
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 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,welldefinedness 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, Ktheoryof the suspension of a C*algebra, the isomorphism K_1(A) \cong K_0(SA), quasihomomorphisms 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 ofPimsnerVoiculescu 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 
Tea (11.05 
Lecture 2 (11.30 
Lunch (1.00 
Lecture 3 (2.00 
Tea (3.35 
Discussion (4.00 
Snacks 


(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  HarishChandra 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.
 A simplified schematic map of Madras, showing the major roads and Hotels and marking the area in which the CIT Campus is located.
 A postscript version of this figure if you want to download it to print at your end.
 A detailed Madras map.
 A gzipped postscript version of this figure
 A schenatic map of the location of IMSc within CIT Campus and its environs
 Detailed map of the location of IMSc within CIT Campus and other landmarks in the Greater Adyar area.
The Institute of Mathematical Sciences is located in a campuslike 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.