IST Algebra (2015) - Speakers and Syllabus

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 one-to-one 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.

Time-Table

  Mon, 7 Dec Tue, 8 Dec Wed, 9 Dec Thu, 10 Dec Fri,11 Dec Sat, 12 Dec
09.30-11.00 HA HA HA HA HA HA
11.00-11.30 Tea Tea Tea Tea Tea Tea
11.30-01.00 SRG SRG SRG SRG SRG SRG
01.00-02.00 Lunch Lunch Lunch Lunch Lunch Lunch
02.30-03.30 HA,MD,PS SRG,MD,PS HA,MD,PS SRG,MD,PS HA,MD,PS SRG,MD,PS
03.30-04.00 Tea Tea Tea Tea Tea Tea
04.00-05.00 HA,MD,PS SRG,MD,PS HA,MD,PS SRG,MD,PS HA,MD,PS SRG,MD,PS
05.00-05.30 Tea Tea Tea Tea Tea Tea
 
  Mon, 14 Dec Tue, 15 Dec Wed, 16 Dec Thu, 17 Dec Fri, 18 Dec Sat, 19 Dec
09.30-11.00 JKV JKV JKV JKV JKV JKV
11.00-11.30 Tea Tea Tea Tea Tea Tea
11.30-01.00 IS IS IS IS IS IS
01.00-02.00 Lunch Lunch Lunch Lunch Lunch Lunch
02.30-03.30 JKV,MD,PS IS,MD,PS JKV,MD,PS IS,MD,PS JKV,MD,PS IS,MD,PS
03.30-04.00 Tea Tea Tea Tea Tea Tea
04.00-05.00 JKV,MD,PS IS,MD,PS IS,MD,PS IS,MD,PS JKV,MD,PS IS,MD,PS
05.00-05.30 Tea Tea Tea Tea Tea Tea

 

Speaker
Affiliation		 No. of
Lectures		 Detailed Syllabus
H. Ananthnarayan
IIT Bombay		 6
  • Lecture 1: permutation groups, alternating groups
  • Lecture 2: dihedral groups, groups of matrices, quaternions etc.
  • Lecture 3 : group homomorphism theorems, examples
  • Lecture 4: Group actions, class equation, conjugacy classes in symmetric groupsand partitions, class equation of A_5.
  • Lecture 5 : Sylow Theorems,
  • Lecture 6: groups of order 12
Sudhir Ghorpade
IIT Bombay		 6
  • Lecture 1: Examples of rings
  • Lecture 2: Ideals and homomorphism theorems
  • Lecture 3: Quotient filed of an integral domain
  • Lecture 4: Maximal and prime ideals
  • Lecture 5: Weak and Strong Nullstellensatz
  • Lecture 6: description of algebraic subsets of the affine plane

Indranath Sengupta
IIT Gandhinagar

 6
  • Lecture 1+2: UFD, PID, Euclidean domains,
  • Lectures 3+4: primes ideals in imaginary quadratic fields
  • Lecture 5+6: applications to number theory.
J. K. Verma
IIT Bombay		 6
  • Lecture 1+2 : Isometries and finite groups of rigid motions of plane,
  • Lectures 3+4: Orthogonal matrices and rotations of space
  • Lecture 5: Groups of symmetries of Platonic solids.
  • Lecture 6: Finite subgroups of SO(3)

Tutorial Assistants

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