Toric Ideal of Polyominoes

Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 11.00 a.m.

• Francesco Romeo - PhD in Mathematics

Abstract:

Polyominoes are two-dimensional objects that were originally used in recreational mathematics and combinatorics, e.g. they are discussed in tiling problems of the plane. A polyomino is a plane figure, obtained by joining squares of equal sizes, called cells. From a Commutative Algebra point of view, the Polyomino ideal is generated by the inner 2-minors of the polyomino. An open problem is to determine whether the above ideal is prime. In recent papers, the primality of some classes of polyomino ideals is proved by passing through the toric ideal, a very relevant object in Algebraic Geometry.
In this talk, we present the toric ideal of the classes above and recent work on the primality of the polyomino ideal.

The seminar corresponds to the first year Ph.D. exam of the course “Algebraic Geometry II”.

Supervisor: Eduardo Luis Sola Conde