Real Analysis and its Applications to Approximation and Learning Theory (2026)

Convener(s)
Name:	Prof. A. Swaminathan	Prof. B. Praba	Dr. A. Sathish Kumar	Dr. S. Yugesh
Mailing Address:	Professor Deparment of Mathematics IIT Roorkee, Roorkee 247667	Professor & Head Department of Mathematics SSN College of Engineering, Kalavakkam , Tamil Nadu. 603 110	Assistant Professor Deparment of Mathematics IIT Madras, Chennai 600 036	Assistant Professor Department of Mathematics SSN College of Engineering, Kalavakkam ,Tamil Nadu, 603 110
Email:	a.swaminathan at ma.iitr.ac.in	prabab at ssn.edu.in	sathishkumar at iitm.ac.in	yugeshs at ssn.edu.in

Real Analysis forms the foundation of modern mathematics and plays a central role in various branches of analysis, with significant applications in approximation theory and learning theory. A solid understanding of real analysis is essential not only for exploring the structure and properties of functions and spaces, but also for developing rigorous methods in approximation and data-driven learning.

The instructional school aims to provide participants with a guided tour of the core concepts in Real Analysis and their connections to Approximation Theory and Learning Theory. It will also introduce advanced tools and applications such as best approximation, Padé approximation and real analytic functions, Shannon’s sampling theorem, convergence of sampling operators, the universal approximation theorem, reproducing kernel Hilbert spaces, and convergence analysis of regularized learning algorithms.

The topics are chosen to give participants exposure to both classical and modern perspectives in analysis and its applications, thereby strengthening their background for further research in mathematics, applied analysis, and data science.

Dates:

Monday, June 1, 2026 - 19:00 to Saturday, June 13, 2026 - 19:00

Venue:

Sri Sivasubramaniya Nadar College of Engineering

Venue Address:

Sri Sivasubramaniya Nadar College of Engineering
Rajiv Gandhi Salai(OMR), Kalavakkam – 603 110, Tamil Nadu.

Venue State:

Tamil Nadu

Venue City:

kalavakkam

PIN:

603110

Syllabus:

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Prof. K. Sumesh Department of Mathematics IIT Madras	6	Review of the real number system, Infimum and Supremum, Euclidean spaces and Metric spaces, Open and closed sets, Limit points, Bolzano-Weierstrass theorem, liminf and limsup of a sequence.
Dr. Surjit Kumar Department of Mathematics IIT Madras	6	Compactness, Characterization of compact sets, Heine Borel theorem, Cauchy sequence and Complete metric space
Dr. G. Arunkumar Department of Mathematics IIT Madras	6	Limits of functions, Continuous functions, Types of discontinuities, Uniform continuity, Differentiable functions and Mean value theorem, Convergence of sequences and series of numbers.
Prof. A. Swaminathan Department of Mathematics IIT Roorkee	6	Sequences and series of functions, Weierstrass M-test, Uniform convergence and its relation to continuity, Differentiation, and integration, Continued fractions, Fundamental results, Convergence, Best approximation and applications, Pade approximation and Real analytic functions.
Dr. A. Sathish Kumar Department of Mathematics IIT Madras	6	Approximation of real valued functions, Bernstein operators and its properties, Weierstass approximation theorem, Korovkin theorem, Shannon sampling theorem, Convergence of sampling operators and Universal approximation theorem.
Prof. S. Sivananthan Department of Mathematics IIT Delhi	6	Reproducing kernel Hilbert space, Gaussian kernel and their RKHSs, Mercer’s theorem, Probabilistic inequalities, Tikhonov-type regularization, Representer theorem and Convergence analysis of regularized learning algorithm.

References:

L. Lorentzen and H. Waadeland, Continued Fractions, Volume 1: Convergence Theory, Atlantis Studies in Mathematics, 2^ndedition, World Scientific, 2008.
H. N. Mhaskar and D. V. Pai, Fundamentals of Approximation Theory, Narosa Publishing House, 2007.
W. Rudin, Principles of Mathematical Analysis, Mcgraw-Hill, 1976.
G. F. Simmons, Topology and Modern Analysis, Kreiger, 2003.
D. F. Walnut, An Introduction to Wavelet Analysis, Birkhauser Boston, MA, 2003.
D-X. Zhou and F. Cucker, Learning Theory: An Approximation Theory Viewpoint, Cambridge University Press, 2007.

Name of the tutors:

S. No.	Name	Affiliation
1	Dr. S. Yugesh	Assistant Professor, Department of Mathematics, SSN College of Engineering
2	Dr. M. Sundarakannan	Assistant Professor, Department of Mathematics, SSN College of Engineering
3	Mr. Nitin Bartwal	Research Scholar, Department of Mathematics, IIT Madras
4	Ms. Puja Sonawane	Research Scholar, Department of Mathematics, IIT Madras
5	Mr. Arpan Kumar Dey	Research Scholar, Department of Mathematics, IIT Madras
6	Mr. M. Surya	Research Scholar, Department of Mathematics, IIT Madras

Time Table:

Day	Date	Lecture 1 (9.30–11.00)	Tea (11.00-11.30)	Lecturer 2 (11.30–01.00)	Lunch (1.00 – 2.30)	Tutorial 1 (2.30-3.30)	Tea (3.30 -4.00)	Tutorial 2 (4.00-500)	Snacks (5.00 – 5.30)

		(Speaker’s name)		(Speaker’s name)		(Speaker’s name)		(Tutor’s name)
Mon	01.06.26	KS		GA		KS, NB, AKD		GA, NB, AKD
Tue	02.06.26	KS		GA		KS, NB, AKD		GA, NB, AKD
Wed	03.06.26	KS		GA		MSK, MS, PS		MSK, MS, PS
Thu	04.06.26	KS		GA		MSK, MS, PS		MSK, MS, PS
Fri	05.06.26	SK		ASK		SK, SY, MSK		MSK, SY, PS
Sat	06.06.26	SK		ASK		SK, SY, MSK		ASK, SY, MSK
Sunday
Mon	08.06.26	ASK	Tea (11.00-11.30)	SK	Lunch (1.00 – 2.30)	ASK, NB, AKD	Tea (3.30 -4.00)	PS, NB, AKD	Snacks (5.00 – 5.30)
Tue	09.06.26	ASK		SK		SY, MS, PS		SY, MS, PS
Wed	10.06.26	AS		SS		NB, PS, MS		SS, MS, AKD
Thu	11.06.26	AS		SS		SY, NB, AKD		SS, NB, AKD
Fri	12.06.26	SS		AS		PS, NB, AKD		AS, NB, AKD
Sat	13.06.26	SS		AS		AS, SY, MS		SY, MS, PS

Full forms for the abbreviations of speakers and tutors:

AS: Prof. A. Swaminathan

SS: Prof. S. Sivananthan

KS: Dr. K. Sumesh

SK: Dr. Surjit Kumar

GA: Dr. G. Arunkumar

ASK: Dr. A. Sathish Kumar

SY: Dr. S. Yugesh

MSK: Dr. M. Sundarakannan

NB: Mr. Nitin Bartwal

PS: Ms. Puja Sonawane

AKD: Mr. Arpan Kumar Dey

MS: Mr. M. Surya

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	67498	Mr. Indra Bate	Male	National Institute of Technology Karnataka	PhD Student	Indian Institute of Technology Kanpur	2016
2	67499	Dr. Radhakrishnan Mohanasundaram	Male	SRM University AP	Assistant Professor	Ramanujan Institute for Advanced Study in Mathematics, University of Madras	2011	19/10/2020
3	67514	Ms. Ronnie Kenneth Athota	Female	Indian Institute of Technology Madras	Jurior Research Fellow	Central University of Tamil Nadu	2025
4	67552	Mr. Thangeshwaran M	Male	PERIYAR UNIVERSITY CENTRE FOR POSTGRADUATE AND RESEARCH STUDIES, DHARMAPURI-635205.	GUEST LECTURER	PERIYAR UNIVERSITY	2013
5	67561	Ms. Aanchal .	Female	Banasthali Vidyapith	PhD	Banasthali Vidyapith	2023
6	67596	Ms Chanchal Sharma	Female	Banasthali Vidyapith	PhD	Chaudhary Charan Singh University	2024
7	67641	Dr. Suresh Kumar M	Male	The Gandhigram Rural Institute-Deemed to be University	Assistant Professor	Manonmaniam Sundaranar University	2010	01/05/2018
8	67648	Ms Aishwaraya .	Female	MIT Art, Design, and Technology University, Pune	ASSISTANT PROFESSOR	Malviya national institute of technology Jaipur, India	2017	26/10/2024
9	67663	Dr. Nirvin Prasath	Male	JEPPIAAR ENGINEERING COLLEGE	Assistant Professor	St. Joseph college, Trichy – 620002.	2014	20/05/2022
10	67683	Dr. Mohammad Arshad	Male	KCC Institute of Technology and Management - Greater Noida	Assistant Professor	Aligarh Muslim University, Aligarh	2019	20/03/2025
11	67701	Ms Vandna Sharma	Female	Banasthali Vidyapith	Ph.D Student	Banasthali Vidyapith	2016
12	67712	Mr Pandiyaraj Elumalai	Male	AGURCHAND MANMULL JAIN COLLEGE	Assistant Professor	University of Madras (M.Sc)	2013
13	67774	Mr. Muniyasamy M	Male	National Institute of Technology Karnataka	PhD Research Scholar	M.Sc at Pondicherry University	2019
14	67789	Ms. Thinkal V	Female	National Institute of Technology	PhD	Amrita Vishwa Vidyapeetham	2023
15	67807	Dr Surjeet Kaushik	Male	Sreenidhi University	Assistant Professor	Indian Institute of Technology Hyderabad	2014	05/08/2018
16	67961	Mr. Deepak Kumar	Male	Govt.,PG College Ambala Cantt	Asst. professor	kurukshetra university kurukshetra	2006
17	68016	Mr. Vijay R	Male	National Institute of Technology Puduchery	PhD student	Central University of Kerala	2022
18	68019	Dr. Muthuvel K	Male	Guru Nanak College	Assistant Professor	University of Madras	2007	24/09/2024
19	68060	Ms Sumaiya Parveen	Female	Aligarh Muslim University	PhD	Shibli College Azamgarh	2018
20	68169	Mr. Nikhil Rai	Male	INDIAN INSTITUTE OF TECHNOLOGY, ROORKEE	PhD	IIT BHUBANESWAR	2025
21	68222	Mr. Sureshkrishnan K	Male	INDIAN INSTITUTE OF TECHNOLOGY ROORKEE	PhD	Pachaiyappas College for Mens, Chennai	2020
22	68638	Dr. Sethuraman Balaji	Male	Vellore Institute of Technology CHennai Campus	Assistant Professor	Anna University	2011	08/04/2019
23	68688	Dr Jayagopal R	Male	Vellore Institute of Technology, Chennai	Assistant Professor	Loyola College (University of Madras)	2012	28/09/2017
24	68830	Dr. Sourav Mandal	Male	NIT DURGAPUR	CSIR RESEARCH ASSOCIATE	UNIVERSITY OF NORTH BENGAL	2018	08/08/2025
25	68966	Mr. Gaurav Aggarwal	Male	Jaypee Institute of Information Technology, Noida	Assistant Professor	IIT Delhi	2014	15/03/2022
26	68971	Mr Lakshmanan S	Male	Central University of Tamil Nadu	PhD Student	Pondicherry University	2020
27	69039	Mrs. Kaleeswari P	Female	VYASA ARTS AND SCIENCE WOMEN'S COLLEGE	ASSISTANT PROFESSOR	AYYA NADAR JANAKI AMMAL COLLEGE, SIVAKASI	2013
28	69068	Ms. Oviya R	Female	St. Xavier's College (Autonomous)	PhD	Loyola College (Autonomous), Chennai, 600034	2024
29	69072	Mr. Amarthya A	Male	St.Xavier's College (Autonomous) , Palayamkottai	PhD	Loyola College, Chennai	2024
30		Mr. E. Arunkumar		Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam

How to Reach:

TBA

School Short Name:

raaaalt

Last Date Application:

Sunday, May 28, 2023

School Type:

IST