**KOÇ UNIVERSITY MATHEMATICS SEMINAR**

**Speaker :** Ayesha Asloob Qureshi, Sabancı University

**Title :** Algebraic structures arising from isotonian maps between posets

**Date : **March 23, 2017 Thursday

**Time : **16:00

**Cookie & Tea : **CASE 124 15:45

**Place : **CASE 124

**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.