Annual Seminar for Mathematics Research Scholars
Date: Friday, 06 October 2023
Time: 11:00 AM
Venue: Lecture Hall 801
On Knutson Ideal and Polyomino
Nirmal Kotal
Chennai Mathematical Institute.
06-10-23

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Abstract

Consider a polynomial f with square-free leading term and construct a class of ideals that is closed under addition, intersection, and colon. Conca-Varbaro and Seccia extensively studied this class of ideals and called them "Knutson ideals", as they were first studied by A. Knutson. We will discuss some algebraic properties e.g. Grobner basis, radicality, F-splitting, etc. of these ideals. A polyomino is a set of unit squares on the plane which is made by joining the squares side by side. Qureshi associated a binomial ideal with polyomino. Relating algebraic properties of these ideals with corresponding combinatorial descriptions of polyominoes is of great interest. We will show that some classes of polyomino ideals are Knutson.

This is an ongoing joint project with Mitra Koley and Dharm Veer.