[Turkmath:760] Seminar by Anargyros Katsampekis at SU

[Canan Kasikci (Alumni)]

Dear All,

Dr. Anargyros Katsampekis from MSGSU will hold a seminar at Sabancı
University on "*A combinatorial approach for determining the binomial
arithmetical rank of a toric ideal*" on Tuesday, November 17 at 15:45, in
FENS 2008.

All interested are welcome to attend. For directions to Sabancı University
please visit:

http://www.sabanciuniv.edu/en/transportation/shuttle-hours

*Abstarct: *

Toric ideals are binomial ideals which represent the algebraic relations of
finite sets of power products. They have applications in diverse areas in
mathematics, such as algebraic statistics, codingtheory, hypergeometric
differential equations, graph theory, etc. A basic problem in Commutative
Algebra asks one to compute the least number of polynomials needed to
generate the toric ideal up to radical. This number is commonly known as
the arithmetical rank of a toric ideal. A usual approach to this problem is
to restrict to a certain class of polynomials and ask how many polynomials
from this class can generate the toric ideal up to radical. Restricting the
polynomials to the class of binomials we arrive at the notion of the
binomial arithmetical rank of a toric ideal. In the talk we study the
binomial arithmetical rank of the toric ideal *I**G*  of a finite graph *G *in
two cases:

(1) G is bipartite,

(2)  *I**G*  is generated by quadratic polynomials.

Using a generalized notion of a matching in a graph and circuits of toric
ideals, we prove that in both cases, the binomial arithmetical rank equals
the minimal number of generators of *I**G*.

greetings

canan kaşıkcı
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