Analysis and Geometry (2022)

Venue:	Bishop Heber College, Tiruchirappalli, Tamil Nadu
Date:	25th, May 2022 to 31st, May 2022

School Convener(s)
Name	Prof. Shrihari Sridharan	Dr. V. Franklin
Mailing Address	School of Mathematics IISER Thiruvananthapuram (IISER-TVM) Maruthamala P.O., Vithura, Thiruvananthapuram. PIN 695 551.	Department of Mathematics Bishop Heber College Puthur, Tiruchirappalli. PIN 620 017.

List of the actual speakers:

Name of the speaker	Position	Affiliation and address
Prof. S. Thangavelu (ST)		Department of Mathematics Indian Institute of Science, Bangalore. (IISc)
Prof. E.K. Narayanan (EKN)		Department of Mathematics Indian Institute of Science, Bangalore. (IISc)
Prof. Shrihari Sridharan (SS)		Indian Institute of Science Education and Research Thiruvananthapuram.(IISER-TVM)

List of the actual tutors:

Name of the tutor	Position	Affiliation and address
Prof. V. Franklin		Department of Mathematics, Bishop Heber College
Prof. Shrihari Sridharan		Indian Institute of Science Education and Research Thiruvananthapuram.(IISER-TVM)

Syllabus:

Actual syllabus covered by each speaker:

Name of the Speaker	:	Detailed Syllabus
Prof. S. Thangavelu (ST), IISc, Bangalore		Real Analysis: Metric spaces, Bolzano Weierstrass theorem, Cantor intersection theorem, Heine- Borel theorem, Continuity, compactness and connectedness, Topological spaces, Basis for a topology, Order topology.
Prof. E.K. Narayanan (EKN) , IISc, Bangalore		Complex Analysis: Analytic functions, Complex integration, Residue calculus, Schwarz’ lemma, Riemann mapping theorem.
Prof. Shrihari Sridharan (SS), IISER-TVM,		Geometry of the upper half-plane: Axioms of non-Euclidean geometry, Mobius maps as isometries, Semi-circles and vertical straight lines on the upper half-plane as distance minimising paths, triangles, polygons, circles; Area formula (Gauss-Bonnet), Fuchsian groups and fundamental domains.

Time Table

Actual time-table that was followed during the programme:

	Lecture 1 (9.30 a.m. – 11.00 a.m)	Tea 11.00 a.m. – 11.20 a.m.	Lecture 2 (11.20 a.m. – 12.50 p.m.)	Tea 12.50 p.m. – 2.20 p.m.	Lecture 3 (2.20 p.m. – 3.50 p.m.)	Tea 3.50 p.m. – 4.10 p.m.	Tutorial (4.10 p.m. -5.10 p.m.)	Snacks 5.10 p.m. – 5.30 p.m.
Day 1 25.5.2022	ST		EKN		SS		T
Day 2 26.5.2022	ST		EKN		ST		T
Day 3 27.5.2022	ST		SS		EKN		T
Day 4 28.5.2022	ST		SS		ST		T
Day 5 30.5.2022	EKN		SS		EKN		T
Day 6 31.5.2022	SS		EKN		SS		T

List of actual Participants

Serial	SID	Full Name	Gender	Affiliation	Position in College/ University	Year of Passing M.Sc./M.A	Ph.D. Degree Date
1	37202	Mr. Askar Hussain	Male	Aligarh Muslim University	PhD	2017
2	37466	Mr. M Muthuvel	Male	Bishop Heber College (Autonomous)	Assistant professor	2014
3	37468	Mr. M Suresh Kumar	Male	Bishop Heber College	Assistant Professor	2007
4	37489	Mr. Sahayaraj joseph Nirmalkumar	Male	St.Xavier's college	Assistant professor	2014
5	37548	Mr Gokul R	Male	Bharathidasan University	PhD Scholar	2020
6	37685	Ms. Nithiya K S	Female	Vellore Institute of Technology	TRA	2009
7	37722	Mr. Kumar C	Male	Vellore Institute of Technology	Assistant Professor (Junior)	2014
8	37737	Dr. Parthiban Saminathan	Male	Bishop Heber College	Assistant Professor	2013	12/06/2020
9		Dr. M. Antony Raj		Department of Mathematics, Bishop Heber College, Trichy.	Assistant Professor
10		Dr. M. Cruz Assistant		Department of Mathematics, Bishop Heber College, Trichy.	Assistant Professor
11		Mr. M. Muthuvel		Department of Mathematics, Bishop Heber College, Trichy.	Assistant Professor
12		Mr. S. Samuel Nirmalsingh		Department of Mathematics, Bishop Heber College, Trichy.	Research Scholar
13		Mr. G. Karthick		Department of Mathematics, Bharathidasan University, Trichy.	Research Scholar
14		Mr. M. Varadharaj		Department of Mathematics, VIT, Vellore.
15		Ms. T. M. C. Priyanka		Department of Mathematics, VIT, Vellore.
16		Mr. A. Agathiyan (APJ)		Department of Mathematics, VIT, Vellore.
17		Dr. K. Saravana Sankar (PDF)		Department of Mathematics, Anna University, Chennai.

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