Equivariant ideals and their membership problem

Prelegent(ci)

Arka Ghosh

Afiliacja

LaBRI, Université de Bordeaux

Język referatu

angielski

Termin

11 czerwca 2025 14:15

Pokój

p. 5440

Tytuł w języku polskim

Equivariant ideals and their membership problem

Seminarium

Seminarium „Teoria automatów”

---

For an infinite set X (of variables) and a group G acting on X, an ideal J in the polynomial ring K[X] in X over the field K is called equivariant (w.r.t. G) if J is invariant under the action of G. We give a necessary and a sufficient condition on the action of G on X for the following extension of Hilbert's basis theorem: every equivariant ideal in K[X] is finitely generated. The equivalence between these conditions is a well-known conjecture by Pouzet. We also prove that a mild strengthening of the sufficient condition implies decidability of the equivariant ideal membership problem: given a polynomial f and a finite set of polynomials H, decide whether f is in the equivariant ideal generated by H.

The first result is a joint work with Sławek Lasota. The second one is a joint work with Aliaume Lopez.

The talk will be divided into two parts. In the first part I will recall classical concepts and results such as Hilbert's basis theorem, Gröbner basis and Buchberger's algorithm. In the second part I will explain how to extend them in the equivariant setting.

---