Functional Analysis (2021)

Convener(s)
 
Name: Prof. M. A. Sofi Dr. Mukhtar Ahmad Khanday
Mailing Address: JKIMS (Kashmir University)
Srinagar-190006		 Associate Professor
Department of Mathematics
Kashmir University)
Srinagar-190006
Email: aminsofi at gmail.com khanday at uok.edu.in


The Teachers Enrichment Workshop is conducted by the National Centre for Mathematics (NCM) to introduce college mathematics teachers to interesting topics in the basic subjects they teach at graduation level. This particular workshop aims to benefit teachers of different colleges in and around Jammu and Kashmir. Apart from lecture sessions there are one hour discussion sessions also which give participants an opportunity to solve exercises and clear their queries.

Click here to download poster.

Dates: 

Sunday, November 28, 2021 - 19:00 to Sunday, December 12, 2021 - 19:00

Venue: 

Venue City: 

Chrono Order: 

384

Syllabus: 

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

1.Prof. Thamban Nair,
IIT Madras

Prof. Pradipta Bandopadhyay.
ISI, Kolkatta

9 hours

A quick Introduction to Banach spaces and bounded linear maps, Uniform boundedness principle (with some applications to classical analysis), Open mapping theorem (Closed graph theorem), Hilbert space (orthonormal systems, orthogonal basis, bounded linear maps), Gram Schmidt orthogonalisation process (applied to certain concrete sequences in spaces), Projection Theorem, Riesz representation theorem for Hilbert space

2.Prof. Sameer Chavan,
Indian Institute of Technology (IIT) Kanpur.

5 hours

Unitary operators and the unitary group on Hilbert space, Spectral theorem self adjoint operators, Hilbert space methods in function theory (including Maximum modulus theorem, Muntz-Szas theorem for

 

3.Dr. Surinderpal Singh
Panjab University, Chandigarh

6 hours

Arzela-Ascoli theorem, Banach-Mazurkiewicz theorem on the size of C\ND. Hausdorff -Alexandroff theorem: (Each compact metrics space as a quotient of the Cantor set), Banach Mazur theorem (C[0,1] as a universal separable Banach space), Computation of the dual of C(K) for K = [0,1] and K = compact subset of ℝ as a prelude to the Riesz Representation Theorem for C(K), K a compact metric space.

 

4.Prof. M. A. Sofi
JKIMS (Kashmir University) Srinagar

7 hours

Background material and motivation, Weak, weak* topologies on Banach spaces, Banach - Alaoglu theorem and applications, Analytic and geometric forms of the HBT and their equivalence, Applications of HBT, Invariant form of HB-theorem, Construction of universal, finitely additive invariant measures on ℝ and .

References:

  1. (Prof. Sameer Chavan)
    (i) Operator Analysis: Hilbert Space Methods in Complex Analysis, J. Agler, J. E. McCarthy,N. J. Young, Cambridge University Press,2020.
    (ii) Simon, Operator Theory. A Comprehensive Course in Analysis, Parts I andV, American Mathematical Society, Providence, RI, 2015,
    (iii) J.B. Conway, A course in Functional Analysis, Springer, 2006.

  1. (Prof. Pradipta Bandopadhyay)

  1. S. Kumaresan and D. Sukumar, Functional Analysis, Narosa.

  2. R. Bhatia, Notes on Functional Analysis, Hindustan Book Agency

  3. M. Fabian et al, Banach Space Theory, Springer Verlag

 

  1. Dr. Surinder Pal Singh Kainth)
    (a) Arzela Ascoli theorem (reference (iv)).
    (b) Hausdorff–Alexandroff Theorem (Proposition 2.3, reference (ii))
    (c)     Riesz Representation Theorem for C(K) when K = [0,1] or a compact subset of ℝ (reference (i)).
    (d)     Riesz Representation Theorem for C(K) when K is a compact metric space (reference (ii))
    (e) Banach-Mazur Theorem. (page 18 of reference (iii)).

References:

  1. Rafael del Rio, A. L. Franco, and J. A. Lara; An approach to F. Riesz representation Theorem, CUBO A Mathematical Journal, 20 (2), 2018, 1-12.
  2. V. S. Sunder; The Riesz Representation Theorem, Indian Journal of Pure and Applied Mathematics, 39 (6), 2008, 467-481.
  3. F. Albiac, N. J. Kalton; Topics in Banach space theory, Springer, 2006
  4. W. Rudin; Principles of mathematical analysis, McGraw-Hill, 1976. 

 

  1. Prof. M. A. Sofi

  1. M. Fabian et al, Banach Space Theory, Springer Verlag

  2. Some Problems in functional analysis inspired by Hahn Banach theorem, Annals of Functional Analysis, 5(2014) no.2, 1-29.

  3. Weak* topology, compactness and the existence of certain invariant measures, Mathematics Newsletter (Ramanujan Math Soc), 31(2), 49-61, Sept. 2020.

 

Tutors:

S. No.

Name

Affiliation

1

Dr. Ramiz Reza/Dr. Nisar A. Lone

IIT Jammu/JKIMS, Srinagar

2

Dr. Ajay Kumar

IIT Jammu

Guest Speaker:

S. No.

Name

Affiliation

1

Prof. Thamban Nair

Department of Mathematics, IIT Madras

 

Note: All the speakers shall be expected to provide notes of their lectures.

Time Table: 

Time-table-I (Sundays):

Day

Date

Lecture-1

(10-11.30)

Tea

(11.35-11.55)

Lecturer 2

(12.00–1.00)

Lunch

(1.30 – 3.00)

Lecture 3

(3.00-4.00)

Discussion

(4.15-5:15)

Tea & Snacks
(5.30 – 6.00)

 

 

(Speaker’s name)

 

(Speaker’s name)

 

(Speaker’s name)

(Tutor’s name)

 

Sun

Nov.28

TN

Tea

TN

Lunch

SC

Discussion (TN+

 

Sun

Decc.5

MAS

Tea

TN

Lunch

Guest Lecture

Discussion (SC+

Snacks

Sun

Dec.12

Discussion (SPS)

Tea

MAS

Lunch

Panel Discussion on Teaching and Research in UG-Maths (All the speakers + participants)

Snacks

 

Time Table-II (Weekdays)

 

Day

Date

Lecture /Discussion
(6.00-7.30)

Mon

Nov.29

SC

Tue

Nov.30

SC

Wed

Dec.1

PB

Thurs

Dec.2

PB

Fri

Dec.3

PB

Sat

Dec.4

MAS

Mon

Dec.6

MAS

Tue

Dec.7

Discussion (MAS)

Wed

Dec.8

SPS

Thurs

Dec.9

SPS

Fri

Dec.10

SPS

Sat

Dec.11

Guest Lecture (TN)

 

 

 

Speakers

 

TN: Prof. Thamban Nair (IIT Madras)

 

PB: Prof. Pradipta Bandopadhyay (ISI, Kolkatta)

 

SC: Prof. Sameer Chavan (IIT Kanpur)

 

SPS: Dr. Surinder Pal Singh Kainth (Panjab University, Chandigarh)

 

MAS: Prof. M A Sofi, JKIMS (Kashmir University), Srinagar

 

 

Selected Applicants: 

 

Serial 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 36956 Mr Sameer Ahmad Gupkari Male Jammu and Kashmir Institute of Mathematical Sciences, Srinagar Assistant Professor University of Kashmir 2003  
2 36957 Ms Uzma Mubeen Female Central university of Kashmir, Ganderbal PhD University of Kashmir 2012  
3 36960 Ms. Raihana Rashid Female Central University of Kashmir Ph. D Scholar University of Kashmir 2015  
4 36988 Mr. Mudassir Ahmad Bhat Male Govt. Degree college Boys Anantnag Assistant Professor University of Kashmir 2009  
5 36991 Mr. Firdous Ahmad Mala Male Govt. Degree College Sopore, J&K Assistant Professor University of Kashmir 2007  
6 37009 Mr. Rohit Pokhrel Male Sikkim Govt. College, Tadong Assistant Professor Sikkim University 2019  
7 37016 Mr. Altaf Ahmad Bhat Male Islamic University of Science and Technology,Awantipora, J and K Assistant Professor University of Kashmir 2008 30/09/2019
8 37020 Dr. Namreen Rasool Female SP College Assistant Professor University of Kashmir 2002 07/05/2013
9 37022 Dr Faroz Ahmad Bhat Male University of Kashmir Assistant Professor University of Kashmir 2007 15/11/2018
10 37033 Dr. Henna Altaf Female Govt. Degree Vollege Lecturer Aligarh Muslim University 2016 09/09/2020
11 37039 Mrs. G Petchiammal Female V.H.N Senthikumara Nadar College Assistant Professor Madurai Kamaraj University, Madurai 2012  
12 37056 Dr. Mushtaq Ahmad Bhat Male NIT Srinagar Assistant Professor University of Kashmir 2011 15/09/2015
13 37062 Dr Farooq Ahmad Sheikh Male Govt College For Women Nawakadal Srinagar asst.Prof University of Kashmiri 2008 14/06/2014
14 37063 Dr. Aadil Hussaain Hussain Dar Male Govt. Degree College Baramulla Lecturer(Contractual) AMU 2014 30/04/2021
15 37069 Dr. Rameez Raja Male National Institute of Technology Srinagar Assistant Professor University of Kashmir    
16 37106 Ms. Manika Gupta Female Kerala School of Mathematics, Kozhikode MSc Student Kerala School of Mathematics, Kozhikode    
17 37108 Mr. S. Viswanathan Male Kerala School of Mathematics MSc. Student Kerala School Of Mathematics Appeared / Awaiting Result  
18 37121 Mr. Ganesh Jayantrao Dharmadhikari Male IGNOU PGDAST STUDENT IISER TVM 2020  
19 37146 Mr. Bhuban Chandra Deuri Male Rajiv gandhi University PhD Rajiv gandhi University 2015  
20 37148 Mr. Patel Jatinkumar G Male Dept. of Mathematics PhD SPU, VVNAGAR 2014  
21 37152 Dr. Shallu Sharma Female University of Jammu Asst. Prof. University of Jammu 2001 05/09/2007
22 37186 Dr Mohd Iqbal Bhat Male University of Kashmir South Campus Asst. Professor University of Kashmir 2000 13/12/2004
23 37195 Dr Tawheeda Rasool Female Government College of Education IASE assistant professor M.sc 2006 30/06/2014
24 37216 Mr. Guddu Kumar Male T. P. COLLEGE MADHEPURA Assistant Professor IISER KOLKATA    
25 37235 Mr. Shivam Kumar Agrawal Male Indian Institute of Technology Kharagpur PhD Indian Institute of Technology Kharagpur 2020  
26 37251 Dr Ishfaq Ahmad Malik Male University of Kashmir Assistant Professor University of Kashmir 2010 22/07/2019
27 37254 Dr Mohamd Saleem Lone Male University of Kashmir Assit. Prof      
28 37272 Dr. Sarfaraz Mohd. Male Department of Mathematics, Jaypee Institute of Information Technology Sector 128 Assistant Professor M.Sc. 2012 01/12/2018
29 37286 Dr. Rajaji Ramasamy Male Patrician College of Arts and Science Assistant Professor Bharathidasan University 2011 06/07/2017
30 37291 Ms. Saloni Gupta Female Iit jodhpur Research assistant jrf Iit gandhinagar 2019  
31 37293 Dr. Gyan Chandra Singh Yadav Male University of Allahabad, Allahabad. Assistant Professor University of Allahabad 2004 05/06/2010
32 37297 Ms. Ritu Nigam Female Indian Institute Of Technology, Kharagpur. PhD Indian Institute Of Technology, Kharagpur. 2019  
33 37302 Dr Sajad Hussain Ahangar Male Government Degree College Shopian Assistant Professor University of Kashmir Srinagar 2007 27/06/2016
34 37304 Dr. Bilal Ahmad Chat Male IUST-Awantipora Pulwama Assistant Professor- Mathematics University of Kashmir 2012 01/11/2016
35 37306 Mr. Bilal Ahmad Dar Male Govt. Degree College Pulwama Assistant Professor Kashmir University 2010  
36 37336 Mr. Arnab Kayal Male Indian Institute of Technology Jodhpur PhD Indian Institute of Technology Hyderabad 2019  
37 37348 Mr. Satyajit Sahoo Male UTKAL UNIVERSITY RESEARCH SCHOLAR UTKAL UNIVERSITY 2013  
38 37363 Ms. Taimun Qaisar Female United Arab Emirates university PhD University of Kashmir 2018  
39 37389 Ms. Rupali Kumari Female NIT, ROURKELA PhD MSc 2018  
40 37399 Mr. Aritra Roy Male BHU PhD Banaras Hindu University 2020  

 

 

 

School Short Name: 

fa

Last Date Application: 

Monday, November 25, 2019

School Type: 

TEW

Separate faculty form: 

0