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Commutative Algebra Webinar
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وبینار جبر جابجایی
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TITLE
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Algebraic Aspects of Polyominoes
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LECTURER
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Ayesha Asloob Qureshi
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Sabanci University, Turkey
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TIME
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Thursday, August 5, 2021,
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18:00 - 20:00
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VENUE |
Lecture Hall 1, Niavaran Bldg.
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SUMMARY |
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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 minors
(also called Polyomino ideals). This class of ideals widely generalizes the ideal
of 2-minors of a matrix of indeterminates, and even the ideal of 2-minors of twosided
ladders. It also includes the meet-join ideal of planar distributive lattices.
Typically one determines for such ideals their Grobner bases, determines their
resolution and computes their regularity, checks whether the rings defined by them
are normal, Cohen-Macaulay or Gorenstein.
Let $P$ be a collection of cells, $K$ be a field and $S$ be the polynomial ring over $K$
in the variables xa with $a ∈ V(P)$, where $V (P)$ is the vertex set of $P$. We denote
by $I_P ⊂ S$ the ideal generated by the inner minors of $P$ and by $K[P]$ the quotient
ring S=IP. We will investigate the algebraic and homological properties $K[P]$ for
given different shapes of $P$.
https://zoom.us/join
Meeting ID: 908 611 6889
Passcode: 210810
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تهران، ضلع جنوبی
ميدان شهيد باهنر (نياوران)، پژوهشگاه
دانشهای بنيادی، پژوهشکده رياضيات
School of
Mathematics, Institute for Research in
Fundamental Sciences (IPM), Niavaran
Bldg., Niavaran Square, Tehran
ipmmath@ipm.ir
♦ +98 21
22290928 ♦
math.ipm.ir |
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