[Turkmath:5618] Symbolic Computation Istanbul Meetings - May 13

[Türkü Özlüm Çelik]

Dear all,

Here is an announcement of the upcoming SCIM talk.
You may find the details of the talk below,
                           also the IMBM (Istanbul Center for Mathematical
Sciences) poster attached.

*Speaker:* Ayesha Asloob Qureshi (Sabancı University)
*Time:* May 13, 17:00 (Istanbul)
*Place:* IMBM and Zoom (hybrid)

*Title:* A conjecture on the Hilbert series of binomial ideals associated
with simple polyominoes

*Abstract:* We will discuss certain types of binomial ideals arising from
combinatorial structures.
In particular, focus will be on the binomial ideals arising from

(1) certain sets of 2-minors of a matrix of indeterminates (also known as
polyomino ideals);

(2) incomparable elements in finite distributive lattices (also known as
join-meet ideals). We will
present a conjecture on the reduced Hilbert series of the coordinate ring
of a simple polyomino
ideal in terms of particular arrangements of non-attacking rooks that can
be placed on the
polyomino. By using a computational approach, the conjecture holds for all
simple polyominoes
up to rank 11. By using an algebraic approach, the conjecture holds true
for the class of parallelogram
polyomino ideals, by looking at those as join-meet ideals of simple planar
distributive lattices.

We will also give a combinatorial interpretation(in terms of Motzkin paths)
of the Gorensteinnes of
parallelogram polyomino ideals.

This talk is based on a recent joint work with Francesco Romeo and
Giancarlo Rinaldo.

References:

1) A.A.Qureshi, F. Romeo, G. Rinaldo, ”Hilbert series of Parallelogram
Polyominoes”, arXiv:2111.01907

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Zoom link:
https://sfu.zoom.us/j/64536080348?pwd=cGZURkY2TDVBaXM5VW1JWTZXOHVyQT09

Meeting ID: 645 3608 0348
Password: scimtalk

Best wishes,
Türkü
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