Koç University, Mathematics Seminar

Date & Time: Thursday, March 23, 16:00-17:00

Place: CASE 124

Speaker:  Ayesha Asloob Qureshi, Sabancı University
 

Title: Algebraic structures arising from isotonian maps between posets

Abstract: Our main goal is to study the ideal L(P,Q) and toric ring K[P,Q] whose generators are in bijection to the isotone maps from P to Q. We examine the several algebraic properties of L(P,Q) including Alexander duality behaviour. The class of algebras

K[P,Q], called isotonian, are natural generalizations of the so-called Hibi rings. We determine the Krull dimension of these algebras and for particular classes of posets P and Q we discuss their normality behaviour. Also, we determine special classes of P and Q for which defining ideal of K[P,Q] admits a quadratic Gröbner basis.

Speaker's Brief Biography: Ayesha Asloob Qureshi got her PhD in Mathematics from Abdus Salam School of Mathematical Sciences of Government College University in Lahore, Pakistan in 2012. She had post doctoral positions at Abdus Salam International Centre of Theoretical Physics in Trieste, Italy and at Osaka University in Japan. Currently, she is a faculty member at Sabancı University. Her research interest lies in the intersection of Commutative and Computational Algebra, Combinatorics and Algebraic Statistics.