IST Commutative Algebra (2016) - Speakers and Syllabus

Speakers :

Sr. Name Affiliation
1 Amartya Kumar Dutta ISI Kolkata
2 Dilip Patil IISc Bangalore
3 Ananthnarayan Hariharan IIT Bombay
4 S. M. Bhatwadekar Bhaskaracharya Pratishthan, Pune
5 Ganesh Kadu Savitribai Phule Pune University

Course associates :

Sr. Name Affiliation
1 Asawari Abhyankar IIT Bombay
2 Dilpreet Kaur  
3 Deepa Krishnamurthi MIT College, Pune
4 Jatin Majithia College of Engineering Pune

Syllabus :

Module-1 : Affine Space and Algebraic Sets, The Ideal of a Set of Points, Hilbert  Basis Theorem, Irreducible Components of an Algebraic Set, Varieties, Radical Ideals, Hilbert’s Nullstellensatz, Coordinate Rings, Krull dimension of ring.

Module-2 : Extension and Contraction of ideals, Nilradical, Jocobson radical, Noetherian rings, Artinian rings, primary decomposition of ideals.

Module-3 : Localization, Integral extensions, going up theorem, Noether’s Normalization lemma, rings of algebraic integers, Dedekind domains.

Module-4: Modules, definition and examples, operations on modules, direct sum and products, finitely generated modules, free modules, Nakayama’s lemma.

 

Abstract of the Lectures :

(i) Amartya Kumar Dutta : Affine Space and Algebraic Sets, The Ideal of a Set of Points, Hilbert Basis Theorem, Irreducible Components of an  Algebraic Set, Varieties, Radical Ideals.

(ii) S. M. Bhatwadekar: Hilbert’s Nullstellensatz, Coordinate Rings, Krull  dimension of ring, localization.

(iii) Dilip Patil : Extension and Contraction of ideals, Nilradical, Jacobson  radical, Noetherian rings, Artinian rings, primary decomposition of ideals.

(iv) Ananthnarayan Hariharan : Integral extensions, going up theorem, Noether’s Normalization lemma, rings of algebraic integers, Dedekind domains.

(v) Ganesh Kadu : Modules, definition and examples, operations on modules, direct sum and products, finitely generated modules, free modules, Nakayama’s lemma.

 

References :

i) Commutative Algebra, N.S. Gopalkrishnan.

ii) Introduction to Commutative Algebra, M.F. Atiyah and I G Mcdonald.

First Week : 28th Novt o 3rd December 2016

Day 9:30- 11:00 11:00- 11:30 11:30- 1:00 1:00- 2:30 2:30-3:30 3:30- 4:00 4:00-5:00 5:00- 5:30
Mon AD Tea DP Lunch AD/JM/DKM Tea AD/JM/DKM Snacks
Tue AD Tea DP Lunch DP/JM/DKM Tea DP/JM/DKM Snacks
Wed AD Tea DP Lunch AD/JM/DKM Tea AD/JM/DKM Snacks
Thu AD Tea DP Lunch DP/JM/DKM Tea DP/JM/DKM Snacks
Fri AD Tea DP Lunch AD/DK/AA Tea AD/DK/AA Snacks
Sat GK Tea SMB Lunch DP/DK/AA Tea DP/DK/AA Snacks

 Second Week : 5th Dec to 10th Dec 2016

Day 9:30- 11:00 11:00- 11:30 11:30- 1:00 1:00- 2:30 2:30-3:30 3:30- 4:00 4:00-5:00 5:00- 5:30
Mon AH Tea GK Lunch GK/JM/DKM Tea GK/JM/DKM Snacks
Tue AH Tea SMB Lunch AH/DK/AA Tea AH/DK/AA Snacks
Wed AH Tea GK Lunch AH/DK/AA Tea AH/DK/AA Snacks
Thu AH Tea SMB Lunch GK/DK/AA Tea GKDK/AA Snacks
Fri AH Tea GK Lunch AH/AA/GK Tea AH/AA/GK Snacks
Sat GK Tea SMB Lunch GK/AA/JM Tea GK/AA/JM Snacks

 

  • AD: Amartya Kumar Dutta
  • SMB: S. M. Bhatwadekar
  • JM: Jatin Majithia
  • AA: Asawari Abhyankar
  • DP: Dilip Patil
  • AH: Anathnarayan Hariharan
  • GK : Ganesh Kadu
  •  DK: Dilpreet Kaur
  • DKM: Deepa Krishnamurthi