Group Theory with Applications to Geometry : This school will cover theory of groups and rings with applications to geometry and number theory. After review of basic group theory, group actions, class equations, Sylow theorems will be discussed. Groups of order 12 will be classified. Applications of matrix groups to study of symmetries, rotations of plane and space will be presented culminating in classification of platonic solids.
Ring Theory with Applications to Number Theory : Basic notions of rings, ideals and homomorphism theorems will be recalled. Theory and examples of UFDs, PIDs and Euclidean domains will be discussed. Hilbert's Nullstellensatz for complex numbers leading a proof of onetoone correspondence between radical ideals and algebraic sets will be presented. A description of prime ideals in rings of integers in quadratic fields leading to applications to Diophantine equations will be presented.
TimeTable
Mon, 7 Dec  Tue, 8 Dec  Wed, 9 Dec  Thu, 10 Dec  Fri,11 Dec  Sat, 12 Dec  
09.3011.00  HA  HA  HA  HA  HA  HA 
11.0011.30  Tea  Tea  Tea  Tea  Tea  Tea 
11.3001.00  SRG  SRG  SRG  SRG  SRG  SRG 
01.0002.00  Lunch  Lunch  Lunch  Lunch  Lunch  Lunch 
02.3003.30  HA,MD,PS  SRG,MD,PS  HA,MD,PS  SRG,MD,PS  HA,MD,PS  SRG,MD,PS 
03.3004.00  Tea  Tea  Tea  Tea  Tea  Tea 
04.0005.00  HA,MD,PS  SRG,MD,PS  HA,MD,PS  SRG,MD,PS  HA,MD,PS  SRG,MD,PS 
05.0005.30  Tea  Tea  Tea  Tea  Tea  Tea 
Mon, 14 Dec  Tue, 15 Dec  Wed, 16 Dec  Thu, 17 Dec  Fri, 18 Dec  Sat, 19 Dec  
09.3011.00  JKV  JKV  JKV  JKV  JKV  JKV 
11.0011.30  Tea  Tea  Tea  Tea  Tea  Tea 
11.3001.00  IS  IS  IS  IS  IS  IS 
01.0002.00  Lunch  Lunch  Lunch  Lunch  Lunch  Lunch 
02.3003.30  JKV,MD,PS  IS,MD,PS  JKV,MD,PS  IS,MD,PS  JKV,MD,PS  IS,MD,PS 
03.3004.00  Tea  Tea  Tea  Tea  Tea  Tea 
04.0005.00  JKV,MD,PS  IS,MD,PS  IS,MD,PS  IS,MD,PS  JKV,MD,PS  IS,MD,PS 
05.0005.30  Tea  Tea  Tea  Tea  Tea  Tea 
Speaker Affiliation 
No. of Lectures 
Detailed Syllabus 
H. Ananthnarayan IIT Bombay 
6 

Sudhir Ghorpade IIT Bombay 
6 

Indranath Sengupta 
6 

J. K. Verma IIT Bombay 
6 

Tutorial Assistants
S. No.  Name  Affiliation 
1  Mrinmoy Datta  IIT Bombay 
2  Parangama Sarkar  IIT Bombay 