TEW  Analysis and Geometry (2020)
Speakers and Syllabus
Name of the Speaker with affiliation 
No. of Lectures 
Detailed Syllabus 
Prof. K.R. Arun (KRA) 
6 
Real Anasis: Metric spaces, Bolzano  Weierstrass theorem, Cantor intersection 
Prof. E.K. Narayanan (EKN) 
6 
Complex Analysis: Analytic functions,Complex integration, Residue calculus , Schwarz’ lemma, Riemann mapping theorem. 
Prof. Shrihari Sridharan (SS) 
6 
Geometry of the upper halfplane: Axioms of nonEuclidean geometry, Mobius maps as isometries, Semicircles and vertical straight lines on the upper halfplane as distance minimising paths, triangles, polygons, circles; Area formula (GaussBonnet). 
References:
1. S. Kumaresan, Topology of Metric spaces, 2nd Ed., Narosa Publishing House, Reprint 2018
2. E. M. Stein, R. Shakarchi, Complex Analysis. Princeton University Press, 2003.
3. S. Katok, Fuchsian Groups. University of Chicago Press. 1992.
Time Table
Day 
Date 
Lecture 1 (9.30 11.00) 
Tea (11.0011.30) 
Lecturer 2 (11.30–1.00) 
Lunch (1.002.00)

Lecture 3 (2.153.45) 
Tea (3.454.00) 
Discussion (4.00500) 
Snacks (5.05–5.30) 



(Speaker’s name) 

(Speaker’s name) 

(Speaker’s name) 

(Tutor’s name) 


Mon 
6720 
KRA  EKN  SS  T  
Tue 
7720 
EKN  SS  KRA  T  
Wed 
8720 
SS  KRA  EKN  T  
Thu 
9720 
KRA 
EKN  SS  T  
Fri 
10720 
EKN  SS  KRA  T  
Sat 
11720 
SS  KRA  EKN  T 
Name of the tutors:
S. No. 
Name 
Affiliation 
1 
Mr. Pankaj Dey  IISERTVM 
2 
Ms. Sharvari Neetin Tikekar  IISERTVM 