#### Hall 123

#### Newton's symmetric polynomials and some open problems

#### Neeraj Kumar

##### PDF, IMSc

*The talk will be focused on power sum, elementary symmetric and complete symmetric polynomials (from Macdonald's book). Towards the end, we will*

also talk about Schur polynomials.

Let "S" be a polynomial ring in several variable and "I" an ideal of "S" generated by symmetric polynomials. Then the theme under discussion will

be: irreducibly of symmetric polynomials, dimension of quotient ring S/I, in particular dimension zero ring (i.e. complete intersection rings), and primness of ideal "I". There are some very interesting open conjectures

related to complete intersection rings by Conca, Krattenthaler, Watanabe

and by Fr\"oberg and Shapiro.

We will see the motivation behind these conjectures and partial evidence in support of it, but not the complete proofs. This talk is aimed at

general audience, however occasionally technical terms and arguments may come-up from commutative algebra or from algebraic geometry, or from

number theory.

Done