[Turkmath:547] Subject: 10 Haziran Çarşamba saat 13.00 de Hacettepe'de Dr. Anargyros Katsampekis'in Semineri: Matching in graphs, circuits and toric ideals

[Mesut Şahin]

Aşağıda detayları verilen seminere ilgilenen herkes davetlidir.
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*Tarih (Date) :* 10.06.2015, Çarşamba (Wednesday)

*Saat (Time):* 13:00

*Yer (Place):* Yaşar ATAMAN Seminer Salonu

*Konuşmacı (Speaker):*Dr. Anargyros Katsampekis (MSGSU)

*Başlık (Title) :*Matching in graphs, circuits and toric ideals

*Özet (Abstract) : *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,
integer programming, 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 IG
of a finite graph G in two cases: (1) G is bipartite, (2) IG is generated
by quadratic binomials.

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 IG.

NOT: Konuşma sonunda çay ve pasta ikramı olacaktır.

(P.S.  Tea and cookies will be served after the talk.)

  Mesut Sahin
  Associate Professor
  Department of Mathematics
  Hacettepe University
  TR 06800 Beytepe
  ANKARA - TURKEY
 http://yunus.hacettepe.edu.tr/~mesut.sahin
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