TEW - Analysis and Geometry (2020)

Speakers and Syllabus


Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Prof. K.R. Arun (KRA)
School of Mathematics
Indian Institute of Science Education
and Research Thiruvananthapuram.
(IISER-TVM)

6

Real Anasis: Metric spaces, Bolzano - Weierstrass theorem, Cantor intersection
H e i n e - B o r e l t h e o r e m ,C o n t i n u i t y , c o m p a c t n e s s  and connectedness, Topological spaces, Basis for a topology, Order topology.

Prof. E.K. Narayanan (EKN)
Department of Mathematics
Indian Institute of Science,
Bangalore.
(IISc)

6

Complex Analysis: Analytic functions,Complex integration, Residue calculus , Schwarz’ lemma, Riemann mapping theorem.

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).

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

(11.00-11.30)

Lecturer 2

(11.30–1.00)

Lunch

(1.00-2.00)

 

Lecture 3

(2.15-3.45)

Tea

(3.45-4.00)

Discussion

(4.00-500)

Snacks

(5.05–5.30)

 

 

(Speaker’s name)

 

      

(Speaker’s name)

 

             

(Speaker’s name)

 

(Tutor’s name)

 

 

 

 

 

 

 

Mon

6-7-20

 KRA  EKN  SS    T

Tue

7-7-20

 EKN  SS  KRA    T

Wed

8-7-20

 SS  KRA  EKN    T

Thu

9-7-20

KRA

 EKN  SS    T

Fri

10-7-20

EKN  SS  KRA    T

Sat

11-7-20

SS  KRA  EKN    T

 Name of the tutors:

S. No.

Name

Affiliation

1

 Mr. Pankaj Dey IISER-TVM

2

Ms. Sharvari Neetin Tikekar IISER-TVM

 

 

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