Dear Colleagues and Students,
You are cordially invited to the Algebra Seminar organized by the Department of Mathematics.
Speaker: Ayesha Qureshi (Sabancı)
“ALGEBRAIC PROPERTIES OF L-CONVEX POLYOMINOES”
Abstract: Polyominoes are, roughly speaking, plane figures obtained by joining squares of equal size (cells) edge to edge. We establish a connection of polyominoes to commutative algebra by assigning to each polyomino its ideal of inner 2-minors, called Polyomino ideal. Polyomino ideals widely generalizes the class of ideals of 2-minors of a matrix of indeterminates (determinantal ideals), and even the class of the ideals of 2-minors of two-sided ladders. Polyomino ideals also include the meet-join ideals of plannar distributive lattices. Typically one determines for such ideals their Gr¨obner bases, determines their resolution and computes their regularity, checks whether the rings defined by them are normal, Cohen-Macaulay or Gorenstein.
Let P be a Polyomino, K be a field and S be the polynomial ring over K in the variables xa with a ∈ V (P), where V (P) is the vertex set of P. We denote by IP ⊂ S the ideal generated by the inner 2-minors of P and by K[P] the quotient ring S/IP. We will investigate the algebraic and homological properties of K[P] for L-convex polyominoes P.
It is based on joint work with Viviana Ene, J¨urgen Herzog and Francesco Romeo.
Date: 11 November, 2020
This is an online seminar. To obtain the event link, please send a message to firstname.lastname@example.org