Dear Colleagues and Students,<\/p>\n
You are cordially invited to the Algebra Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Ayesha Qureshi (Sabanc\u0131)<\/p>\n
\u201cALGEBRAIC PROPERTIES OF L-CONVEX POLYOMINOES\u201d<\/p>\n
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\u00a8obner bases, determines their resolution and computes their regularity, checks whether the rings defined by them are normal, Cohen-Macaulay or Gorenstein.
\nLet P be a Polyomino, K be a field and S be the polynomial ring over K in the variables xa with a \u2208 V (P), where V (P) is the vertex set of P. We denote by IP \u2282 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.
\nIt is based on joint work with Viviana Ene, J\u00a8urgen Herzog and Francesco Romeo.<\/p>\n
Date: 11 November, 2020
\nTime: 14:00<\/p>\n
This is an online seminar. To obtain the event link, please send a message to sezer@fen.bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
Dear Colleagues and Students, You are cordially invited to the Algebra Seminar organized by the Department of Mathematics. Speaker: Ayesha Qureshi (Sabanc\u0131) \u201cALGEBRAIC PROPERTIES OF L-CONVEX POLYOMINOES\u201d Abstract: Polyominoes are, roughly speaking, plane figures obtained by joining squares of equal size (cells) edge to edge. We establish a connection of [\u2026] <\/p>\n