Groebner bases of determinantal ideals II
组织者
方明
, Manolis Tsakiris
,
袁北彗
演讲者
Chenqi Mou
时间
2024年04月06日 09:30 至 11:30
地点
AMSS-N208
摘要
In this talk I will introduce determinantal ideals, which are multivariate polynomial ideals generated by specific minors of a generic matrix, and their Gröbner bases with respect to the (anti-)diagonal term orders. The determinantal ideals this talk will cover include traditional, ladder, and Schubert determinantal ones. For traditional determinantal ideals, I will present how the Robinson-Schensted-Knuth (RSK) correspondence from combinatorics, combined with the straightening law, can be applied to study their Gröbner bases; for Schubert determinantal ideals defined for permutations, which is a fundamental algebraic concept in the study of Schubert calculus, I will show how to construct their Fulton generators from the permutations and identify them as Gröbner bases with respect to the anti-diagonal term orders. If time permits, I will also briefly present our recent works on the reduced Gröbner bases of Schubert determinantal ideals.