Séminaire Calcul Formel

Gröbner theory of Grassmannian cluster algebras

par Dr Lara Bossinger (Mathematics Institute of the National Autonomous University of Mexico)

Europe/Paris
https://bbb.unilim.fr/b/vac-m6r-7dv

https://bbb.unilim.fr/b/vac-m6r-7dv

Description

In this talk I will report on joint work with Fatemeh Mohammadi and Alfredo Nájera Chávez. For a (multi-)homogeneous ideal inside a polynomial ring we generalize classical Gröbner degenerations to define a multi-parameter family combining all Gröbner degenerations associated with a maximal cone in the Gröbner fan and all its faces. When this construction is applied to the homogeneous coordinate ring of the Grassmannians Gr(2,n) and Gr(3,6) (presented compatible with their cluster structure) the algebra defining the family for a certain maximal Gröbner cone coincides with the universal coefficient cluster algebra. I will review the basic notions needed from Gröbner theory and cluster algebras, explain our general construction and our (computational) results for the Grassmannians.