East
African Summer School on Commutative Algebra and Algebraic Geometry
August 9-20, 2004
University of Nairobi, Kenya
Part I : An introduction to Algebraic Geometry and
Combinatorial
Methods in representation theory.
Main topics:
- The Grassmann variety and its Schubert Cells
- Plücker coordinates and their quadratic equations
- The standard monomial basis of Hodge associated to Plücker
coordinates
- The theory of standard bitableaux
- Representations of the linear and symmetric group
Notes
Part II : Ideals, varieties and algorithms
Main topics:
(i) Groebner basis basics orderings on
monomials
- Division algorithm in the polynomial ring
- Monomials Ideals and Dickson’s lemma
- Hilbert Basis Theorem and Groebner Basis
- Buchberger’s algorithm
- Ideal membership problem, implication problem and elimination
theory
- The geometry of elimination
(ii) Invariant theory of finite groups
- Symmetric polynomials
- Finite matrix groups and rings of invariants
- Generators for the ring of invariants
(iii) Applications
- Most computer work will be done by using the computer algebra
package CoCoA.
- Besides the main minicourses, several other topics in computer
algebra and also some experiments of computer assisted research will be
offered.
Notes