AIS Operator Theory (2014)

Venue: Indian Statistical Institute, Bangalore
Dates: 2nd to 21st Jun, 2014

 

Convener(s) Speakers, Syllabus and Time table Applicants/Participants

 

School Convener(s)
Name Prof. T. S. S. R. K. Rao Dr. J.  Sarkar
Mailing Address Indian Statistical Institute,
R V College Post,
Bangalore-560059
 Indian Statistical Institute,
 R V College Post,
Bangalore-560059

 

Speakers and Syllabus 

A brief Description :
In this advanced program we plan to cover rapidly in the first week,
Basic Functional Analysis, Hilbert space theory, and cover theory of Bounded linear Operators on Hilbet spaces, concrete operators on specific Hilbert spaces, theory of unbounded operators, including spectral theorems.

The second and third  weeks will be devoted to Differential operators, Basics of spectral theory for bounded operators on Banach spaces and concrete operators and matrices -Toeplitz /Wigner types.
Six lectures on Complex geometry and Hilbert space operators, Bounded and compact composition operators on Orlicz and  Banach Function spaces. Hardy space  H^2 (D),  Littlewood subordination Principle, bounded and compact composition operators on H^2 (D) and norm estimates.

Time permitting some future research directions will be indicated by all speakers.

Syllabus:

Speakers Lectures Detailed Syllabus
T. S. S. R. K. Rao
ISI		 7 Fundamental Concepts:  Banach space theory, Basic theory of Hilbert spaces and operators on Hilbert spaces.
 J. Sarkar
ISI		  7  

Operators on specific Hilbert function spaces, invariant subspaces.
 Pl Muthuramalingan
ISI		  6 Theory of unbounded operators and spectral theorems.
 K B Sinha
JNCAR		  6  Types of unbounded operators, differential operators and several examples.
 M. N. Namboodiri, CUSAT  8  Basics of spectral theory for bounded operators on Banach spaces
and concrete operators and matrices -Toeplitz /Wigner types.
 T. Bhattacharya, IISc  7 Talk 1: Positive definite kernels, reproducing kernel Hilbert spaces,examples, Sz.-Nagy dilation of a single contraction: an    existential proof.

Talk 2: An actual construction of the minimal isometric dilation due to Schaeffer. Realization formula for H-infinity functions of norm no greater than one.

Talk 3: Ando's dilation for a pair of commuting contractions. Ando's proof. von Neumann's inequality for a single contraction and for a pair of commuting contractions.

Talk 4: A different proof of Ando dilation for a pair of commuting matrices due to Agler and McCarthy. Distinguished variety of the bidisk. The interaction with geometry begins.

Talk 5: The symmetrized bidisc: geometric properties.

Talk 6 &7: A pair of commuting operators with the symmetrized bidisc as the spectral set. Its fundamental operator. Normal boundary dilation.
Romesh Kumar, Jammu  8  Bounded and compact composition operators on Orlicz and  Banach Function spaces. Hardy space  H^2 (D),  Littlewood subordination Principle, bounded and compact composition operators on H^2 (D) and norm estimates.

 

Time-Table(Fillininitialsofspeakersandcourseassociates):

 

 

Lecture 1

Tea

Lecturer 2

Lunch

Lecture 3

Tutorial

Day

Date

10-11:00

 

11:30-12-30

 

2:00-3:00

3.30-5.30

Mon

2June 2013

TSS1

 

TSS2

 

JS1

 

Tue

3June2013

JS2

 

TSS3

 

TSS4

 

Wed

4June2013

JS3

 

JS4

 

TSS5

 

Thu

5June2013

PLM1

 

PLM2

 

TSS6

 

Fri

6 June 2013

MNN1

 

JS5

 

PLM2

 

Sat

7 June 2013

TSS7

 

JS6

 

MNN2

 

Mon

09June2013

PLM3

 

PLM4

 

JS7

 

Tue

10June2013

KBS1

 

MNN3

 

PLM5

 

Wed

11June2013

KBS2

 

RK1

 

KBS3

 

Thu

12June2013

MNN4

 

MNN5

 

RK2

 

Fri

13June2013

RK3

 

KBS4

 

KBS5

 

SAT

14 June2013

TB1

 

RK4

 

MNN6

 

Mon

16June2013

KBS6

 

MNN7

 

MNN8

 

Tue

17June2013

RK5

 

TB2

 

RK6

 

Wed

18June2013

TB3

 

RK7

 

TB4

 

Thu

19June2013

RK8

 

TB5

 

Special Lecture

 

Fri

20June2013

TB6

 

TB7

 

Special Lecture

 

Sat

21 June 2013

Special Lectures

 

Special Lectures

 

 

 

 Tutorial Assistants:

S. No.

Name

Affiliation

1

Jayanarayanan

ISI

2

T Paul

IITH

3

Nirupama Mallick

ISI
Selected Applicants

 

Instructions are:

 

  1. Selected candidates will be contacted by e-mail by the organizers with instruction on how to reach the venue.
  2. They will be given a letter for the purpose of getting leave.
  3. No travel expenditure will be reimbursed (No TA/DA).
  4. Free board and lodging on sharing basis will be at ISI BC campus strictly from 1st June Sunday till 21st Saturday.
  5. Get room key on arrival from at security booth.
  6. Candidates are advised to depart post Lunch, Saturday the 1st of June. Stay before or beyond these dates is not possible.

 

Sr. SID Full Name Gender Affiliation  State Position University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A
1 5191 Mr. Santhosh Kumar Pamula Male IIT Hyderabad Andhra Pradesh, Hyderabad Research Scholar University Of Hyderabad (HCU) 2012
2 5212 Mr Sivaramakrishnan  C Male IIT Hyderabad Andhra Pradesh, Hyderabad Research Scholar Department Of Mathematics, Periyar University, Salem, Tamil Nadu 2012
3 5216 Mr Veeramani  . S Male IIT Hyderabad Andhra Pradesh, Hyderabad Not Applicable Manonmaium Sundaranar University 2010
4 5229 Mr Anindya  Ghatak Male National Institute of Science and Research Orissa, Bhubaneswar Ph.D Calcutta University 2012
5 5235 Mr. Savan Ketankumar Patel Male Sardar Patel University Gujarat, Anand Ph.D School of Science, Gujarat University. 2013
6 5250 Mr. Rakshitkumar Shashikant Upadhyay Male Department of Mathematics,Sardar Patel University. Gujarat, Vallabh Vidyanagar Ph.D Department of Mathematics, Sardar Patel University. 2012
7 5259 Mr. Manish Kumar Pandey Male Department of Mathematics, Sardar Patel University Gujarat, Anand Ph.D Sardar Patel University, Ahmedabad 2012
8 5329 Mr. Shankar  P Male Kerala School Of Mathematics Tamil Nadu, Kozhikode Ph.D Pondicherry University 2012
9 5331 Ms. Arundhathi  Krishnan Female IIT Madras Tamil Nadu, Chennai Ph.D Indian Institute of Technology Madras 2012
10 5342 Mr. Ajoy  Jana Male IIT Madras Tamil Nadu, Chennai Ph.D University Of Calcutta. (Dept. Of Pure Mathematics ) 2013
11 5353 Mr Lavy  Koilpitchai Male IIT Madras Tamil Nadu, Chennai Ph.D Pondicherry University 2011
12 5496 Mr. Srijan  Sarkar Male Indian Statistical Institute, Kolkata. West Bengal, Kolkata Ph.D University Of Hyderabad, M.Sc. 2012
13 5542 Ms. Dipti Ratilal Patel Female Department of Mathematics, Sardar Patel University Gujarat, Vallabh Vidyanagar Ph.D Department of Mathematics, Sardar Patel University, V. V. Nagar 2010
14 5570 Mr. Kislay  Kishor Male Jawaharlal Nehru University Delhi, New Delhi Ph.D University of Delhi 2010
15 5586 Ms. Kavitha  R Female Manonmaniam Sundaranar University Tamil Nadu, Tirunelveli Ph.D Manonmaniam Sundaranar University 2011
16 5588 Ms. Jamal  Fathima Female Manonmaniam Sundaranar University Tamil Nadu, Tirunelveli Ph.D Manonmaniam Sundaranar University 2010
17 5603 Mr Janson Antony A Male Chennai Mathematical Institute Tamil Nadu, Chennai Ph.D University of Hyderabad 2013
18 5640 Mr Balesh  K Male Cochin University of Science and  Technology Kerala, Ernakulam Research Scholar Cochin University of Science and Technology 2007
19 5685 Mr. Bijaya Kumar Sahu Male Indian Institute Of Bhubaneswar Orissa, Bhubaneswar Ph.D Utkal University 2009
20 5776 Mr. Nishant  Agrawal Male Indian Institute of Science Education and Research, Mohali Punjab, Sas Nagar MS Student Indian Institute of Science Education and Research, Mohali  Appeared/ Awaiting Result
21 5805 Mr. Hitesh  Gakhar Male IISER Mohali Punjab, Mohali BS-MS IISER Mohali  Appeared/ Awaiting Result
22 5815 Ms. Rachana  Shokhanda Female University of Delhi Delhi, Delhi M.Phil Sri Venkateswara College, University of Delhi , M.Sc. 2013
23 5848 Ms Rani  Kumari Female IIT Kanpur Uttar Pradesh, Kanpur Ph.D Delhi  University  ,  M.A 2009
24 5850 Mr. Mahesh  Kumar Male Lady Shri Ram College For Women, University of Delhi, Delhi. Delhi, New Delhi Asst. Prof. M.Sc.(Math), University of Delhi 2007
25 5857 Ms. Reena Female University of Delhi Delhi, New Delhi

M. Phil

 University of Delhi 2011
Local Candidates*
1 5600 Mr Monojit  Bhattacharjee Male Indian Institute Of Science Karnataka, Bangalore JRF Hyderabad Central University 2011
2 5606 Mr. Somnath  Hazra Male IISc. Bangalore Karnataka, Bangalore Ph.D IIT Delhi 2011
3 5611 Mr. Samir Ch. Mandal Male Indian Institute of Science Karnataka, Bangalore Integrated Ph.D   2013
4 5642 Mr Soumitra  Ghara Male Indian Institute of Science Karnataka, Bangalore Ph.D Indian Institute of Science 2013
5 5820 Mr Md Ramiz Reza Male Indian Institute of Science. Karnataka, Bangalore Ph.D Indian Institute of Science 2011
6 5829 Mr. Rajeev  Gupta Male Indian Institute of Science, Bangalore Karnataka, Bangalore Ph.D Indian Institute of Technology, Delhi 2010

* Will attend lectures with no support

How to reach

  •  By Air
    • Bangalore International Airport is approximately one And a half hour drive from the Institute. It handles direct flights from a number  of national and international destinations. A journey by taxi from the air port to the Institute will cost approximately Rs.900.
  •     By Rail
    • Bangalore, the "Garden city of India" is well connected  with rail and roads. There are plenty of trains from all the major cities of India   to Bangalore City.  Indian Statistical Institute, which is next to the Bangalore University, is about 12 km on the way to Mysore from the city .  A journey by taxi from the railway station to the Institute will take approximately 30 minutes and cost approximately Rs.150.
  •     By Bus
    • The city bus service is known as BMTC (or BTS) and its main terminal is right opposite the city railway station. Please use the subway from outside the railway station to reach the BTS bus station. (The area that covers the railway station, bus station etc. is known as Majestic.) You may take a Kengeri bound bus (nos. 222A, 226A and 403A) from platform no. 19A to come to ISI. Platform no. 19A is closest to the railway station. Ask for a ticket to "Jairamdas Bus stop". (The ISI bus stop is known as 'Jairamdas'.) This bus stop is just after the University Gate bus stop and just before the R. V. College bus stop. The bus journey takes 30-40 minutes.
  •     By Auto/Taxi
    • ISI is approximately 12 km from the Bangalore City railway station. You may hire an auto-rickshaw to reach ISI. Please hire an auto only from the police manned auto-stand just outside the railway station. The meter fare by auto-rickshaw from the railway station to ISI is approximately Rs. 55. However, you may have to pay one and a half times the actual meter fare.
    • If you take an auto at the Railway/Bus station you will soon get on to Mysore Road. You will travel by the side of a long fly-over. End of the fly over is 8 km from ISI. Continue on Mysore Road - After some time you will get the BHEL factory on your right (4 km from ISI) -- continue on Mysore Road - soon you will get the huge Rajarajeshwari Nagar Arch (2 km from ISI) on your left - continue on Mysore Road - after some time you get the Jnanabharathi Campus of the Bangalore University (one km from ISI) on your right - continue on Mysore Road (do not enter the Bangalore University Campus)- Just about one km down Mysore Road, you get a Railway Level Crossing on your right. Enter through the railway gate to reach ISI. Once you get on to Mysore Road, always be on it till you reach the Railway Level Crossing. Next to the railway gate, on Mysore Road, is Azad Coach Builders factory. If, by mistake, you reach the R V College of Engineering, you have gone past ISI by a km. Turn back and start looking for the Railway Level Crossing on your left now.
    • If you arrive during the office hours (9.30 AM to 5.30 PM) contact the Security Officer Sri. Sunderarajan, who will direct you to your room. Outside office hours, you may seek assistance from the security guards at the gates.