Speaker: Adimoolam Chidambaram, Visiting Scholar, Stanford University

One of the fundamental theorems of commutative algebras is Hilbert's basis theorem, a particular case of which states that a polynomial ring R in n variables over a field is Noetherian, i.e. every ideal I of R has a finite basis so that every element of I can be written as a finite linear combination of basis elements with coefficients in R. A Grobner basis of I is a basis which has a number of properties that make it a very powerful tool for effective methods in algebraic geometry and in other areas where one wants to find solutions of a finite set of non-linear equations. The Grobner basis for an ideal is defined using certain order ">" the monomials, satisfying the condition: the leading term of every nonzero element of I is divisible by the leading term of some element of the Grobner basis. A Grobner basis can be considered as a generalization of vector space basis. In this talk, I shall give an introduction to Grobner bases and present some applications.

Please join us beforehand for pizza.