AIS Computational Commutative Algebra (2010)

Speakers

 Syllabus

 0. Review of Commutative Algebra (Rabeya Basu)

1. Basics of Groebner Basis and Monomial Ideals (Clare D'Cruz)

2. Groebner Fan and Polytopes (K.N. Raghavan)

3. Solving Polynomial Equations and Convex Polytopes (J.K. Verma)

4. Coding Theory (S.R. Ghorpade)

5. Invariant theory (R.A. Rao)

6. Integer Programming and Combinatorics (Amitava Bhattacharya)

7. Computational Algorithms in Commutative Algebra (Santiago Laplagne)

8. Computational Algorithms in Algebraic Geometry (Abdenacer Makhlouf)

9. Computational Homological Algebra (Andreas Steenpass)

        REFERENCES / RECOMMENDED BOOKS:

(1) W. Decker, C. Lossen; Computing In Algebraic Geometry. A Quick

Start Using Singular (ACM 16, Springer, 2006)

(2) D. Eisenbud, D. Grayson, M. Stillman M, B. Sturmfels; Computations

 in algebraic geometry with Macaulay-2 (Springer,2001)

(3) G.-M. Greuel, G. Pfister; A Singular Introduction To Commutative

Algebra (2nd Edition)(Springer, 2008)

(4) Notes of the Workshop on Computational Commutative Algebra held

 at the Harish Chandra. Research Institute (HRI), Allahabad, India in

  December 2003.

(5) Notes of the Winter School on Algorithms in Invariant Theory and

Algebraic Geometry held at Dept. of Mathematics, University of Pune,

 India in December 1999.

(6) D. Cox, J. Little, B. O’Shea Donal; Using Algebraic Geometry, Springer

Verlag.

(7) B. Strumfels; Algorithm in Invariant Theory, Springer Verlag, 2008.