Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

 Prof.  B V Rajarama Bhat

(ISI Bangalore Centre)

6 hrs

Basics of (C^*)-algebras, the Gelfand–Naimark theorem, continuous functional calculus, the spectral theorem for normal operators, positive linear functionals, representations and the GNS construction, completely positive maps, and the Stinespring dilation theorem.

 Dr. Bata Krishna Das

(IIT Bombay)

9 hrs

RKHS, Sums and products of kernels, Multiplier algebras on RKHS, Wold decomposition of isometries, transfer function realization of Schur functions and BCL factorization of the Hardy shift, Isometric Dilation of single and n-tuple of commuting contractions, Ando dilation using BCL model and refined von Neumann inequality on distinguished varieties.

 Prof. Jaydeb Sarkar
(ISI Bangalore Centre)

9 hrs

H^p spaces, Beurling's theorem, Model spaces, Characteristic functions, Commutant lifting theorem, Toeplitz operators, Hankel operators, Schur functions and representations of Schur functions, Nevanlinna-Pick interpolations, Schur functions and interpolation on polydisc and ball.

 Dr. Ved Prakash Gupta

(Jawaharlal Nehru University)

9 hrs

Von-Neumann Algebra, von Neumann’s double commutant theorem and Kaplansky’s density theorem, normal linear functionals, geometry of projections in a von Neumann algebra and type decomposition of von Neumann algebras, abelian von Neumann algebras, the GNS construction.

 Dr. Arup Chattopadhyay                       
(IIT Guwahati)

6 hrs

Trace class operators, Schatten Class, Second-order trace formulas, Carey-Helton-Howe-Pincus trace formula, Singular traces and perturbation formulae for tuples of commuting unitaries, Trace formula for contractions.

S. No.

Name

Affiliation

1

Dr.Sibaprasad Barik

ISI Bangalore

2

Dr. Samir Panja

ISI Bangalore

3

Mr. Arghya Chongdar

ISI Bangalore

Day

Date

Lecture 1

(9.30
to
11.00)

Tea

(11.05  to
11.25)

Lecture 2

(11.30
to
1.00)

Lunch

(1.05
to
2.25)

Tutorial

(2.30
to
3.30)

Tea

(3.35 to
3.55)

Tutorial

(4.00
to
5.00)

Snacks

5.05
to
5.30

(name of the speaker

(name of the speaker

(name of the speaker + tutors)

(name of the speaker + tutors)

Tues

15/12/26

BVRB

BKD

BVRB+ ARC+SP

BKD+SB+SP

Wed

16/12/26

BVRB

BKD

BVRB+ ARC+SP

BKD+SB+SP

Thu

17/12/26

BVRB

BKD

BVRB+ ARC+SP

BKD+SB+SP

Fri

18/12/26

BVRB

BKD

BVRB+ ARC+SP

BKD+SP+SB

Sat

19/12/26

BKD

BKD

BKD+ ARC+SP

BKD+SB+SP

SUNDAY: OFF

Mon

21/12/26

JS

VPG

JS+SB+SP

VPG+ARC+SP

Tues

22/12/26

JS

VPG

JS+SB+SP

VPG+ARC+SP

Wed

23/12/26

JS

VPG

JS+SB+SP

VPG+ARC+SP

Thu

24/12/26

JS

VPG

Lecture by AC

VPG+ARC+SP

Fri

25/12/26

JS

VPG

Lecture by AC

AC+SB+SP

Sat

26/12/26

JS

VPG

Lecture by AC

VPG+ARC+SP

Sun

27/12/26

AC

AC

AC+SB+SP

AC+SB+SP