Real and Functional Analysis (2026) | National Centre for Mathematics

Convener(s)


Name:	Prof. Pratulananda Das	Dr. Bikash Chakraborty
Mailing Address:	Professor of Mathematics Department of Mathematics Jadavpur University Kolkata - 700032	Assistant Professor in Mathematics Department of Mathematics Ramkrishna Mission Vivekananda Centenary College Rahara, Khardaha West Bengal Pin – 700118
Email:	pratulananda at yahoo.co.in	bikashchakrabortyy at gmail.com

In this workshop we will deal with two different directions, one being real analysis, in particular Riemann integration followed by measure theory and the other being functional analysis. These topics are being (going to be) taught in the third year and fourth year in Mathematics honours courses (4 year course under NEP which is now being implemented in West Bengal and most states from the year 2023). The main aim is to make the participants aware as to how to introduce these topics to the students in interesting ways with lots of examples and to emphasis the interplay between the topics.

Dates:

Monday, August 17, 2026 - 09:00 to Saturday, August 22, 2026 - 21:00

Venue:

Ramakrishna Mission Vivekananda Centenary College

Venue Address:

Ramakrishna Mission Vivekananda Centenary College
Rahara, Khardaha
West Bengal
Pin – 700118

Venue State:

West Bengal

Venue City:

Rahara

PIN:

700118

Syllabus:

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Prof. Soumalya Joardar (IISER Kolkata)	6	Normed linear spaces and Banach spaces, basic properties, bounded linear operators, duals of normed linear spaces, Hahn Banach theorem, uniform boundedness principle, open mapping and closed graph theorems. Examples and applications
Prof. Jaydeb Sarkar ISI Bangalore	6	Compact operators in Banach spaces and their importance, spectral theorem for compact operators. Integral operators, basic results about these operators. Computational aspects of integral operators, specifically Volterra operator. Applications and examples
Dr. Bikash Chakraborty RKMVCC	6	Riemann Integral, properties of Riemann integrable functions, Fundamental theorems of integral calculus, Mean value theorem, Change of variable in Riemann integration, improper Riemann integration
Prof. Pratulananda Das Jadavpur University, Kolkata	6	Lebesgue outer measure, Extension of the idea of length function, Lebesgue measure, measurable sets, existence of non-measurable sets, idea of measurable functions, Lebesgue integration, advantages over Riemann integration. Applications and examples

References:

1. Topology of metric spaces, S. Kumaresan
2. Topology, J.R. Munkres
3. Topology, J.F. Simmons

(Lecture notes from the speakers, if available)

Name of the tutors:

S. No.	Name	Affiliation
1	TBD	Ramkrishna Mission Vivekananda Centenary College
2	TBD	Ramkrishna Mission Vivekananda Centenary College
3

Time Table:

Day	Date	Lecture 1 (9.30-10.30)	Tea (10.35-10.55)	Lecturer 2 (11.00-12.00)	Lecture 3 (12.00-1.00)	Lunch (1.00 -2.20)	Lecture 4 (2.30-3.30)	Tea (3.35-3.55)	Discussion (4.00-500)	Snacks (5.05 – 5.30)
		(Speaker’s name)		(Speaker’s name)	(Speaker’s name)		(Speaker’s name)		(Tutor’s name)
Mon		PD		SJ	SJ		BC		BC, -, -
Tue		PD		PD	SJ		SJ		SJ, -, -
Wed		BC		SJ	SJ		PD		PD, -, -
Thu		JS		JS	BC		BC		SB, -, -
Fri		PD		BC	JS		JS		JS, -, -
Sat		PD		BC	JS		JS		BC, -, -

Selected Applicants:

Serial	SID	Full name	Gender	Affiliation	Position in College/University	Year of Passing M.Sc./M.A	Ph.D. Degree Date
1	70055	Ms. Aditi Som	Female	University of Calcutta	MSc Student
2	70094	Mr. Sourav Chowdhury	Male	University of Calcutta	Research Scholar	2011
3	70102	Mr. Santu Mondal	Male	University of Calcutta	MSc Student
4	70152	Mr Abhishek Dangal	Male	NBBGC, Sikkim University	MSc Student	Awaiting Result
5	70154	Ms. Kousika Karthikeyan	Female	KPR Institute of Engineering and Technology	Ph.D Student	2022
6	70033	Ms Chanchal Sharma	Female	Banasthali Vidyapith	PhD
7	70051	Prof. Dr Sowndariya R	Female	PPG Institute Of Technology Coimbatore	Assistant Professor	2017	28/10/2025
8	70088	Mr Muniyasamy S	Male	Government Higher Secondary School	Graduate Teacher	2017
9	70104	Ms. Shazia Akhtar	Female	Central University of Kashmir	PhD	2022
10	70109	Mr. Bikram Dholey	Male	Jadavpur University	Research Scholer	2022
11	70115	Mr. Pradip Kevat	Male	University of Lucknow	M.Sc Student	Awaiting Result
12	70119	Mr Lokesh Mishra	Male	Babasaheb Bhimrao Ambedkar University	MSc Student	2025
13	70121	Ms. Aanchal .	Female	Banasthali Vidyapith	PhD	2023
14	70127	Mr. Suman Pal	Male	Kulti College	State Aided College Teacher (Sact)	2018
15	70129	Ms. Maryam Usmani	Female	Department of Mathematics, Aligarh Muslim University	PhD	2023
16	70137	Mr Prasanth S	Male	Chikkana Government Arts Collage Tiruppur	MSc student	Awaiting Result
17	70143	Ms. Mahima Vashishtha	Female	Hindu College	Ph.D.	2020
18	70155	Mr Sekar K	Male	KPR Institute of Engineering and Technology	PhD Research Scholar	2014
19	70160	Ms Soma Sarkar	Female	University of Gour Banga	Msc student	2014
20	70161	Ms. Sandhiya B	Female	KPR Institute Of Engineering And Technology	PhD Student	2024
21	70164	Mr Rajasekaran Kanakkan	Male	KPR Institute Of Engineering And Technology	PhD Student	2023
22	70167	Ms. Sampriti Dey	Female	NIT Durgapur	PhD	2024
23	70168	Ms Varshini D	Female	KPR Institute of Engineering and Technology	Ph.D. Student	2025
24	70170	Mr. Aieshwarya Bihar Chhotaray	Male	SRM University-AP, Amaravati	PhD	2025
25	70171	Ms. Adrita Chakrabortty	Female	SRM University-AP	PhD	2023
26	70173	Dr Prakash Chandra Srivastava	Male	Birla Institute Of Technology Mesra Ranchi Jharkhand	Assistant Professor	2000	05/09/2009
27	70178	Mrs. Sangeetha K	Female	KPR Institute of Engineering and Technology	Ph.D Research Scholar	2009
28	70183	Mr. Ankur Sharmah	Male	Bhattadev University	Assistant Professor	2017	31/05/2023
29	70189	Mr. Onkar Yuvraj Tiruke	Male	National Institute of Technology Meghalaya	MSc Student	2026
30	70190	Mr. Suprakash Pal	Male	NIT Andhrapradesh	PhD	2023	01/06/2026
31	70192	Mr. Ashan Gupta	Male	Munger University, Munger	Assistant Professor	2012
32	70198	Mr Mutharasu V	Male	Chikkanna government arts college tirupur- 02	MSC Student
33	70200	Dr. Chinmay Kumar Giri	Male	Dharanidhar University, Keonjhar	Asst. Prof.	2013	01/12/2018
34	70202	Mr. Niren Biswas	Male	University of Calcutta	PhD Student	2019
35	70207	Mr Malaya Ranjan Meher	Male	National institute of technology, Andhrapradesh	PhD	2025
36	70209	Dr. Dipankar Hazra	Male	Heramba Chandra College	State Aided College Teacher, Category - I	2016	02/04/2025
37	70210	Mr. Chinmay Patra	Male	J.K. College	State Aided College Teacher	2017
38	70211	Mr Chandru S	Male	SRM Institute of Science and Technology	Ph.D Research Scholar	2023
39	70212	Dr. Gopal Dutta	Male	J. K. College	Assistant Professor	2014	17/07/2020
40	70214	Dr. Shailendra Kumar Bharati	Male	D.A.V. PG College, Maharaja Suhel Dev University, Azamgarh, U.P. India	Assistant Professor	2010	31/12/2015
41	70218	Mr. Subunkar Mazumder	Male	Cotton University	PhD	2024
42	70219	Dr Tamiilselvan K	Male	IIIT Sri city	Researcher	2018	26/09/2025
Local Participants
1	70111	Mr Alapan Roy	Male	Ramakrishna Mission Vivekananda Centenary College	MSc Student	2026
2	70122	Mr. Nikhil Chand	Male	Ramakrishna Mission Vivekananda Centenary College	Research Scholar	2022	19/09/2023
3	70147	Mr. Samrat Bhanja	Male	Ramakrishna Mission Vivekananda Centenary College	PhD	2023
4	70149	Mr. Koushik Maity	Male	Ramakrishna Mission Vivekananda Centenary College	PhD	2023
5	70076	Mr. Kalyan Barman	Male	Ramakrishna Mission Vivekananda Centenary College	Research Scholars	2019
6	70085	Mr. Sashadhar Dutta	Male	Ramakrishna Mission Vivekananda Centenary College	Msc
7	70186	Mr. Swarnabha Nandy	Male	Ramakrishna Mission Vivekananda Centenary College, Rahara	M.Sc. Student	2026
8	70213	Mr. Monosij Biswas	Male	Ramakrishna Mission Vivekananda Centenary College	MSc Student	2026
9	70215	Mr. Ritam Sinha	Male	Ramakrishna Mission Vivekananda Centenary College, Rahara	PhD scholar
10	70216	Mr. Suvendu Roy	Male	Ramakrishna Mission Vivekananda Centenary College	PhD	2020

How to Reach:

TBA

School Short Name:

rfa

Last Date Application:

Monday, March 31, 2025

School Type:

TEW