Operator Theory and Operator Algebra (2023)

Convener(s)

 
Name: Dr. Bipul Saurabh, Assistant Professor  Dr. Projesh Nath Choudhury, Assistant Professor
Mailing Address: Discipline of Mathematics
Indian Institute of Technology, Palaj
Gandhinagar – 382355, Gujarat		 Discipline of Mathematics
Indian Institute of Technology, Palaj
Gandhinagar – 382355, Gujarat
Email: bipul.saurabh at iitgn.ac.in projeshnc at iitgn.ac.in

 

Dates: 

Monday, March 6, 2023 - 19:00 to Saturday, March 11, 2023 - 19:00

Venue: 

Venue Address: 

 

Office AB 5/344, Discipline of
Mathematics, IIT Gandhinagar, Palaj,
Gandhinagar – 382355, Gujarat, India

 

 

 

Venue State: 

Venue City: 

PIN: 

382355

Syllabus: 

 Syllabus to be covered in terms of modules of 6 lectures each:

Name of the Speakers with their affiliation.

No. of Lectures

Detailed Syllabus

B. V. Rajarama Bhat (BVR)

Stat-Math Unit, Indian Statistical Institute, Bangalore 560059, Karnataka

2

 Trace Inequalities
Set-theoretic version of some basic dilation results of operator theory. The lectures would cover Wold decomposition, Halmos dilation, Sz. Nagy dilation,inter-twining lifting, commuting and non-commuting dilations,Completely positive maps, Dilation of Hilbert space operators. There will be also discussion of variations on this theme.

K. B. Sinha (KBS)

J. N. Centre for Advanced Scientific Research, Jakkur, Bangalore560064, India, and Indian Statistical Institute, Karnataka

 

2

Gadadhar Misra (GM)

 

Discipline of Mathematics,

Indian Institute of Technology, Palaj

Gandhinagar 382355, Gujarat

 

2

Jaydeb Sarkar (JS)

Stat-Math Unit, Indian Statistical Institute, Bangalore 560059, Karnataka

3

 Brief history of operator theory. Relationship of operators and functions. Introduction to Hardy space on the open unit disc.Shift operator and basic properties. Reproducing kernel Hilbert spaces. Hardy space as a reproducing kernel Hilbert space.Shift invariant subspaces of the Hardy space. Beurling's view, Inner-outer factorizations, and examples.
Introduction to model spaces. Commutant lifting theorem.
Schur functions and representations of Schur functions. Applications - Nevanlinna-Pick interpolations (past-present-future, if time permits).

Examples of some basic C*-algebras and classifications. Applications to system theory/electrical engineering (if time permits).

Sameer Chavan (SC)

Department of Mathematics and Statistics, Indian Institute of Technology Kanpur Kanpur 208016, Uttar Pradesh

3

Bipul Saurabh (BS)

Discipline of Mathematics,

Indian Institute of Technology, Palaj

Gandhinagar 382355, Gujarat

3

C*-algebra, spectrum, Unitization, the Gelfand-Naimark theorem, continuous Functional Calculus, the Serre-Swan theorem, K-groups, Bott periodicity, Spectral triples, Fredholm operators, Fredholm modules, K-homology groups, Index pairing.

Apoorva Khare (AK)

Department of Mathematics,

Indian Institute of Science,

Bengaluru 560012, India, Karnataka

3

 (a) Definitions, examples of total positivity (TP) and Total nonnegativity (TN)

(b) Whitney’s density theorem: TP is dense in TN

(c) Eigenvalues of square TP/TN matrices are positive/nonnegative.

(d) Variation diminishing property and its history

(e) Polya frequency sequences: examples, generating functions, classification

(f) Polya frequency functions: examples, Laplace transform, classification

(g) If time permits: a brief look at the Laguerre-Polya class and Polya-Schur multipliers

 

Projesh Nath Choudhury (PNC)

Discipline of Mathematics,

Indian Institute of Technology, Palaj

Gandhinagar 382355, Gujarat

3

  References:

  1. W. Arveson, An Invitation to C*-Algebras, Graduate Texts in Mathematics, 2011.
  2. J.B Conway, A Course in Functional Analysis, Springer New York, 2019.
  3. A.  Connes, Noncommutative geometry. Academic Press, Inc., San Diego, CA, 1994.
  4. R.G. Douglas, Banach Algebra Techniques in Operator Theory, Graduate Texts in Mathematics, 1998.
  5. R.G. Douglas and V.I. Paulsen, Hilbert Modules Over Function Algebras, Longman Scientific & Technical, 1989.
  6. S. Karlin, Total positivity. Vol. I, Stanford University Press, Stanford, CA, 1968.
  7. A. Khare, Matrix analysis, Pólya frequency functions, and preservers of (total) positivity, Lecture notes.
  8. M. Martin and  M. Putinar, Lectures on Hyponormal Operators, Birkhäuser, 1989.
  9. R.A. Martinez-Avendano and  P. Rosenthal, An Introduction to Operators on the Hardy-Hilbert Space, Graduate Texts in Mathematics, 2007.
  10. B. Sz Nagy, C. Foias, H. Bercovici and L. Kérchy, Harmonic Analysis of Operators on Hilbert Space, Springer New York, 2010.
  11. A. Pinkus, Totally positive matrices, Cambridge University Press, Cambridge, 2010.
  12. M. Rørdam, F. Larsen and N. Laustsen: An Introduction to K-Theory for C*-Algebras,   Cambridge University Press, 2000.

Time Table: 

 Tentative time-table, mentioning names of the speakers and tutors with their affiliation:

Day

Date

Lecture
1

(10:00
to
11.00)

Tea

(11.00
to
11.25)

Lecture 2
(11.30
to
12.30)

Lunch

(12.30
to
1.55)

Lecture
3
(2.00
to
3.00)

Tea

(3.00
to
3.25)

Lecture 4

(3.30
to
4.30)

Tea

(4.30
to
4.55)

Discussion Hour

(5.00
to
6:00)

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

 

 

 

Mon

 

PNC

 

JS

 

BVR

 

KBS

 

JS+BVR

Tues

 

PNC

 

JS

 

BVR

 

KBS

 

JS+BVR

Wed

 

PNC

 

JS

 

BS

 

GM

 

KBS+PNC

Thu

 

AK

 

SC

 

BS

 

GM

 

SC+BS

Fri

 

AK

 

SC

 

BS

 

GM

 

AK+BS

Sat

 

AK

 

SC

 

BS

 

GM

 

SC+GM

 Full forms for the abbreviations of speakers and tutors:

 PNC: Projesh Nath Choudhury

 AK: Apoorva Khare

 JS: Jaydeb Sarkar

 SC: Sameer Chavan

 BS: Bipul Saurabh

 KBS: K. B. Sinha

 BVR: B. V. Rajarama Bhat

 GM: Gadadhar Misra

 

Selected Applicants: 

Sr.n SID Full Name Gender Affiliation Position in College/ University Uni./ Ins. M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 45645 Mr Siddharth Panigrahi Male IIT, Patna PhD Indian Statistical Institute, Bangalore Centre 2021  
2 45649 Mr. Hemant Bansal Male IISER Mohali PhD TIFR CAM 2020  
3 45696 Ms. Sanchita Satpathy Female IISER Mohali Int-phd Student IISER Mohali Awaiting Result  
4 45741 Ms. Stanzin Dolkar Female Central University of Jammu. PhD University of Jammu. 2017  
5 45704 Mr Aashish Kumar Maurya Male IIT Goa PhD IIT Delhi 2021  
6 45747 Mr Santu Bera Male Indian Institute of Technology, Kanpur Ph.D. Student Indian Institute of Technology Kanpur 2020  
7 45766 Ms Suchetana Samadder Female Indian Statistical Institute , Kolkata PhD Indian Institute of Technology , Madras 2021  
8 45778 Mr. Rajkamal Nailwal Male IIT Kanpur PhD IIT Indore 2017  
9 45785 Mr. Bhaskar Paul Male IIT Bhilai Ph.D. student Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math 2021  
10 45803 Mr. Shubham Jain Male Indian Institute of Technology Kanpur PhD Student University of Rajasthan, Jaipur 2017  
11 45804 Mr. Saikat Giri Male Indian Institute of Technology Guwahati. PhD Indian Institute of Technology Bhubaneswar. 2021  
12 45817 Mr. Chaman Kumar Sahu Male Indian Institute of technology Kanpur PhD Indian Institute of technology Bombay 2018  
13 45902 Ms Mansi Anil Suryawanshi Female Indian Statistical Institute, Bangalore PhD University of Pune 2015  
14 45905 Mr. Supratim Jana Male Indian Institute of Technology Guwahati PhD scholar University of Hyderabad 2020  
15 45907 Ms Arpita Mal Female Indian Institute of Science, Bangalore NPDF Jadavpur University 2015 23/09/21
16 45924 Dr. Sushil Singla Male Indian Statistical Institute, Delhi Center Visiting Scientist Shiv Nadar University Delhi NCR 2016 15/03/22
17 45929 Mr. Milan Kumar Mal Male Indian Institute Of Technology Madras PhD Student Jadavpur University 2019  
18 45961 Ms Geeta Chowdhry Female National Institute of Technology Karnataka, Surathkal PhD IISER Mohali 2019  
19 46061 Mr. Ayan Dey Male Indian Statistical Institute Delhi Center PhD Indian Institute of Technology Kanpur 2022  
20 46089 Mr. Debabrata Jana Male IIT Kanpur PhD Banaras Hindu University 2017  
21 46092 Mr. Mo Javed Male Indian Institute of Technology Roorkee PhD Student Indian Institute of Technology Bombay 2019  
22 46098 Ms. Kritika Kritika Female Indian Institute of Technology Roorkee Ph.D Student Indian Institute of Technology Delhi 2022  
23 46108 Ms Sarada Anoushka N K U Female Indian Institute of Technology, Ropar PhD NISER, Bhubaneswar 2022  
24 46115 Ms. Bhumi Shailesh Amin Female Indian Institute of Technology Hyderabad PhD Student The Maharaja Sayajirao University of Baroda 2019  
25 46122 Ms. Manisha Devi Female Dr B R Ambedkar National Institute of Technology, Jalandhar PhD Panjab University, Chandigarh 2018  
26 46171 Ms. Priyanka Darshanlal Aroda Female IIT Bombay PhD Student University of Hyderabad 2020  
27 46212 Mr. Sushobhan Das Male Indian Institute Of Science Bengaluru 2ND Year Int Phd Student IISC Bengaluru Appeared  
28 46222 Mr. Karishman Bhupendrakumar Solanki Male Institute of Infrastructure, Technology, Research and Management (IITRAM) PhD Sardar Patel University 2017  
29 46225 Mr. Saptak Bhattacharya Male Indian Statistical Institute PhD Jadavpur University 2021  
30 46265 Mr. Avadhkumar Bhurabhai Patel Male Deprtment of Mathematics PhD student Sardar Patel University 2017  
 Local  Participants   
1 45700 Mr. Bhuva Akshay Manasukhbhai Male IIT Gandhinagar PhD student The maharaja sayajirao university of baroda 2020  
2 45709 Ms. Shivangi Yadav Female Indian Institute of Technology Gandhinagar Ph.D. National Institute of Technology Rourkela 2020  
3 45824 Ms Shreema Subhash Bhatt Female Indian Institute of Technology-Gandhinagar PhD Student Sardar Patel University, Vallabh Vidyanagar 2018  
4 45951 Mr. Shivajee Gupta Male IIT Gandhinagar PhD Scholar M.Sc. 2017  
5 46062 Mr. Suman Pal Male IIT Gandhinagar MSc Student IIT Gandhinagar Appeared  
6 46068 Ms. Siddhi Balu Ambhore Female Indian Institute of Technology Gandhinagar PhD Indian Institute of Technology Gandhinagar 2020  
7 46102 Mr. Ganesh Jayantrao Dharmadhikari Male IIT Gandhinagar ARYABHATA - HoMI FELLOW IISER TVM 2020  
8 46109 Mr. Raju Nandi Male IIT Gandhinagar POST-DOC IIT MADRAS 2016 08/12/22
9 46251 Mr. Prasad Namdev Pawar Male IIT Gandhinagar PhD IIT Palakkad 2022  
10 46129 Mr. Ashif Khan Male IIT Gandhinagar PhD University of Hyderabad 2021  
Wait-listed  participants
1 45723 Mr. Bappa Ghosh Male Indian Statistical Institute, Kolkata JRF INDIAN STATISTICAL INSTITUTE 2020  
2 45756 Mr. Sureshkumar M Male Indian Institute of Science Education and Research, Bhopal PhD Pondicherry University, Pondicherry 2021  
3 46186 Ms. Vidhya Venugopal Female Bits Pilani, K K Birla Goa Campus PhD MAHATMA GANDHI UNIVERSITY 2014  
4 46130 Mr. Arnab Chattopadhyay. Male Indian Statistical Institute, Delhi Centre. Ph.D. Student. Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math. 2019  
5 45799 Ms Vinaya P C Female Cochin University of Science and Technology PhD Student Cochin University of Science and Technology 2019  
6 46229 Mr. Jatin Girdharlal Patel Male Dept. of Mathematics, Sardar Patel University PhD MSc 2014  
7 46079 Ms. Shanola Smitha Sequeira Female Indian Institute of Technology Hyderabad Ph.D Pondicherry University 2017  
8 46105 Mr. Saikat Das Male Indian Statistical Institute Delhi PhD Indian Institute of Technology Kanpur 2020  

 

 

 

 

 

How to Reach: 

How to reach IIT Gandhinagar

School Short Name: 

wotoa

Last Date Application: 

Monday, August 15, 2022

School Type: 

NCMW

Separate faculty form: 

0