TEW - Analysis and Geometry (2022)

Speakers and Syllabus

S.No Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
1 Prof. S. Thangavelu (ST) Department of Mathematics Indian Institute of Science, Bangalore. (IISc) 6 Real Analysis: Metric spaces, Bolzano- Weierstrass theorem, Cantor intersection theorem, Heine-Borel theorem, C o n t i n u i t y, c o m p a c t n e s s a n d connectedness, Topological spaces, Basis for a topology, Order topology.
2 Prof. E.K. Narayanan (EKN) Department of Mathematics Indian Institute of Science, Bangalore. (IISc) 6 Complex Analysis: Analytic functions, Complex integration, Residue calculus (may be, we will leave this topic out), Schwarz’ lemma, Riemann mapping theorem.
3 Prof. Shrihari Sridharan (SS) Indian Institute of Science Education and Research Thiruvananthapuram. (IISER-TVM) 6 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.

 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) 		T e a

11: 00 - 11: 20

 Lecture 2
(11.20 - 12.50) 		L u n Lecture 3
(2.20 - 3.50) 		T e a
3: 50 - 4: 10		 Tutorial
(4.10 - 5.10) 		S n a c k s
5: 10 - 5: 30
Wed 25/05/22 ST EKN c h SS T
Thu 26/05/22 EKN SS   ST T
Fri 27/05/22 SS ST 12: 50 EKN T
Sat 28/05/22 ST EKN - SS T
Mon 30/05/22 EKN SS 2: 20 ST T
Tue 31/05/22 SS ST   EKN T

 

 Tutors:

1.Prof. P. K. Sanjay, Depertment of Mathematics, National Institute of Technology (NIT) - Calicut.
2.Dr. Sharvari Neetin Tikekar, School of Mathematics, IISER-TVM.

 

 

 

 

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