Transformations & Isometries (2022)

Convener(s)


Name:	Somnath Basu	Shibananda Biswas	Sushil Gorai
Mailing Address:	Associate Professor, IISER Kolkata	Associate Professor IISER Kolkata	Assistant Professor IISER Kolkata
Email:	somnath.basu at iiserkol.ac.in	shibananda at iiserkol.ac.in	sushil.gorai at iiserkol.ac.in

Please Note: Participants have to arrange for their own travel.

This instructional school is aimed at college and university teachers, specializing in mathematics. We aim to cover the topic of isometry from several different points of view. Isometry (and symmtery) is an ubiquitous concept in science that is especially important in mathematics. We want to highlight seemingly different manifestations of isometry in three separate contexts, broadly connected to the three classical geometries: plane, hyperbolic and spherical.

Dates:

Monday, June 6, 2022 - 16:45 to Saturday, June 18, 2022 - 18:30

Venue:

IISER

Venue Address:

Indian Institute of Science Education & Research Kolkata
Mohanpur - 741246, West Bengal, India.

Venue State:

West Bengal

Venue City:

Kolkata

PIN:

741246

Chrono Order:

362

Syllabus:

Name and affiliation of the speaker	Number of lectures	Detailed Syllabus
Shibananda Biswas Associate Professor, IISER Kolkata	8	Isometries of Linear Spaces This part of the school deals with distance and angle preserving maps in R 2 . We shall discuss isometries in R 2 and complex formula of plane isometries, orientations, finite group of plane isometries as well as isometries in R n We will talk about matrix groups, permutation groups and classification of isometries. We will discuss (orthogonal) projection maps and its properties. Finally we discuss finite group of isometries in R 3 and classification of conics under isometries. References: Geometry - Ancient & Modern by J. R. Silvester
Sushil Gorai (Associate professor, IISER Kolkata)	8	Conformal Symmetries This part of the school deals with hyperbolicity of planar domains. We start with classical Schwarz lemma, Schwarz-Pick lemma and computation of the automorphism group of the unit disk. We discuss Poincaré metric on D in details. Schwarz lemma will be revisited from the viewpoint of the Poincaré metric and its curvature. Some complex analysis results like Liouville’s Theorem and Montel’s Theorem will be presented from a geometric viewpoint. A proof of the big Picard Theorem will be discussed. We shall also discuss some new invariant metrics, i.e., Caratheodory and Kobayashi metrics and their isometries on planar domains. We shall also analyze whether auto-morphisms fo the domain give rise to isometries. Hyperbolicity of the domain will be discussed in detail. References: Complex Analysis: The Geometric Viewpoint by S. G. Krantz
Somnath Basu (Associate Professor, IISER Kolkata)	8	Isometries & Gaussian Curvature This part of the school deals with isometries of surfaces embedded in R³.We start with the basics of curves and surfaces in R³,revisiting osculating circles (and planes),Serret-Frenet formula. We discuss curvature (Gaussian and mean) of surfaces in various forms. The first and second fundamental form will be discussed, followed by various implications of the sign of the Gaussian curvature. We shall talk about Gauss-Bonnet theorem and the local-global phenomenon it illustrates. We discuss isometries of a surface, geodesics and some relevant examples (for the three basic prototypes). References: Differential Geometry of Curves & Surfaces by M. Do Carmo, Differential Geometry: A First Course inCurves and Surfaces by T. Shifrin.

Tutors:

Sachchidanand Prasad (PhD student, IISER Kolkata) (tutor for topics B & C)
Sanjoy Chatterjee (PhD student, IISER Kolkata) (tutor for topics A & C)
Golam Mondal (PhD student, IISER Kolkata) (tutor for topics A & B)

Prerequisites: We will assume familiarity with the basic syllabus covered in BSc and MSc on linear algebra, complex analysis, calculus in several variables and basic topology.

Time Table:

	9:30-11:00	11:30-1:00	1:00-2:30	2:30-3:30	4:00-5:00
6/06/22	Lecture A.1	Lecture B.1	L	Tutorial A.1	Tutorial B.1
7/06/22	Lecture B.2	Lecture A.2	U	Tutorial B.2	Tutorial A.2
8/06/22	Lecture C.1	Lecture A.3	N	Tutorial C.1	Tutorial A.3
9/06/22	Lecture A.4	Lecture B.3	C	Tutorial A.4	Tutorial B.3
10/06/22	Lecture C.2	Lecture A.5	H	Tutorial C.2	Tutorial A.5
11/06/22	Lecture B.4	Lecture A.6	-	Tutorial B.4	Tutorial A.6
13/06/22	Lecture A.7	Lecture C.3	L	Tutorial A.7	Tutorial C.3
14/06/22	Lecture B.5	Lecture A.8	U	Tutorial B.5	Tutorial A.8
15/06/22	Lecture C.4	Lecture B.6	N	Tutorial C.4	Tutorial B.6
16/06/22	Lecture B.7	Lecture C.5	C	Tutorial B.7	Tutorial C.5
17/06/22	Lecture C.6	Lecture C.7	H	Tutorial C.6	Tutorial C.7
18/06/22	Lecture B.8	Lecture C.8	-	Tutorial B.8	Tutorial C.8

The lecture titled Lecture X.n means nth lecture on topic X, where X is one of the topics listed in the syllabus. Tutorial X.n will be taken by the speaker for topic X along with the two tutors assigned for topic X.

There will be 12 days of lectures excluding the Sunday (12th June, 2022). For every day of the workshop, there will be 3 hours of lectures together with 2 hours of discussion/tutorial. The classrooms where the lectures will be held will have internet and audio/video facilities to allow for online participants to interact.

Selected Applicants:

The selected participants will be contacted by the organizers regarding the invitation and confirmation of their participation.

List 1
Who will have accommodation

Sr.n	SID	Full Name	Gender	Affiliation	Position in College/ University	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./ M.A	Ph.D. Deg.
1	32694	Dr Kiran Virivinti	Male	osmania University	Assistant Professor	osmania	2002	31/05/2016
2	32815	Dr. N Paramaguru	Male	Government Arts College for Women	Assistant Professor	Annamalai University	2003	11/09/2014
3	32923	Dr. Sarfaraz Sarfaraz	Male	Jaypee Institute of Information Technology, Noida, Sector 128, UP, 201304	Assistant Professor	M.Sc.	2012	28/10/2018
4	32932	Dr. Manoj Sahni	Male	PANDIT DEENDAYAL PETROLEUM UNIVERSITY	Assistant Professor	M.Sc.	2003	07/10/2010
5	32945	Dr. Abhishek Mukherjee	Male	Kalna College	Asst. Prof.	Burdwan University, M.sc.	2007	11/11/2019
6	33323	Dr. Debabrata Chakraborty	Male	J.K. COLLEGE, PURULIA	ASST. PROFESSOR	VISVA BHARATI	2010	02/06/2018
7	33363	Mr. Gopal Dutta	Male	J.K. College, Purulia	ASST. PROFESSOR	IIT GUWAHATI	2014
8	33466	Dr Avijit Sarkar	Male	University of Kalyani	Assistant Professor	University of Kalyani	2002	03/02/2010
9	33513	Dr. Avinoy Paul	Male	Cachar College	Assistant Professor	Gauhati University	2004	01/07/2014
10	33705	Prof Rajasekar S P	Male	Government Arts College for Women	Assistant Professor	Pondicherry University	2004
11	33777	Dr. Akhil Mittal	Male	GUJARAT ARTS AND SCIENCE COLLEGE	Assistant Professor	Department Of Mathematics, The Maharaja Sayajirao University of Baroda	2006	27/12/2018
12	33941	Mr Naveen Gupta	Male	Miranda House, University of Dehi	Assistant professor	Department of mathematics, University of Delhi	2012
13	33975	Dr. Chandru Hegde	Male	Mangalore University	Asst. prof.	Mangalore University	2006	14/07/2018
14	34020	Dr Aftab Hussain Shah	Male	Central university of Kashmir	Assistant professor	AMU Aligarh	2004	12/04/2010
15	37662	Mr. Firdous Ahmad Mala	Male	Government Degree College Sopore, Jammu & Kashmir	Assistant Professor	University of Kashmir	2007
16	38409	Mr. Sapan Gupta	Male	Sri Sathya Sai Institute of Higher Learning	Assistant Professor	IIT Madras	2018
17	38512	Mr. Kuparala Venkata Vidyasagar	Male	SVLNS GOVERNMENT DEGREE COLLEGE BHEEMUNIPATNAM	Lecturer in mathematics	Andhra University	2001
18	38688	Mr Bindumadhaba Mohanty	Male	Radhakrishna Institute of Technology and Engineering	Assistant Professor	Sambalpur University	2014
19	38975	Dr. Surya Prakash	Male	C.M.P. Degree College, University of Allahabad	Assistant Professor	University of Allahabad	2015	20/07/2021
20	38976	Mr. Ajim Uddin Ansari	Male	C.M.P. Degree College, University of Allahabad, Prayagraj	Assistant Professor	University of Allahabad	2015
Local participant (without accommodation)
1	33039	Mr. Subhamoy Mondal	Male	Presidency University	PhD	Calcutta University	2017
2	33524	Mr Nirmal Biswas	Male	University of Kalyani	Ph.D	University of Kalyani	2016
3	33526	Mr. Gour Gopal Biswas	Male	University of Kalyani	Ph.D.	University of Kalyani	2017
4	33867	Mr Bhaskar Mandal	Male	RAHARA RAMAKRISHNA MISSION VIVEKANANDA CENTENARY COLLEGE	research scholar	UNIVERSITY OF HYDERABAF	2017
5	33931	Mr. Ranadip Gangopadhyay	Male	DST-CIMS, BHU	Completed PhD	Netaji Subhas Open University	2013	04/12/2018
6	37431	Mr. Tamoghna Kar	Male	Ramakrishna Mission Vivekananda Educational and Research Institute	MSc Student	Ramakrishna Mission Vivekananda Educational and Research Institute	2022
7	37676	Mr Arnab Kundu	Male	Indian Institute of Information Technology	PhD Student	Ramakrishna Mission Vivekananda Educational and Research Institute	2021
8	38685	Mr. Md Rahil Miraj	Male	Indian Statistical Institute	Second Year B.Math(Hons.) Student
9	38742	Ms. Lekha Das	Female	Indian Institute Of Information Technology, Guwahati	PhD	Ramakrishna Mission Vivekananda Educational And Research Institute, Belur	2021
10	38839	Mr. Rabi Kumar Chakraborty	Male	Indian Statistical Institute,Kolkata	MSc Student	Indian Statistical Institute, Kolkata	Appeared / Awaiting Result
11	39014	Ms Anuvertika Pandey	Female	NISER, Bhubaneswar	PhD student	Banaras Hindu University	2020
12	39015	Ms Saswati Mukherjee	Female	National Institute of science education and research	Phd student	University of Burdwan	2019