[Turkmath:530] Matematik-İstatistik Seminerleri-İEU

[burcu silindir]

Sayın liste üyeleri,



İzmir Ekonomi Üniversitesi, Matematik Bölümü tarafından düzenlenen
Matematik-İstatistik seminerleri kapsamında,  Dr. Anargyros Katsampekis
tarafından 27 Mayıs 2015, saat 14.00'de, M201 nolu sınıfta  “Matching in
graphs, circuits and toric ideals”  başlıklı bir seminer verilecektir.


Seminerin detayları aşağıda belirtilmiş olup tüm ilgilenenler davetlidir.

İyi çalışmalar.

Burcu Silindir Yantır

İzmir Ekonomi Üniversitesi

Matematik Bölümü

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Dear all,

İzmir University of Economics, Department of Mathematics continues its
Mathematics-Statistics seminars on May 27 th, 2015, at 14.00 pm at M201,
with Dr. Anargyros Katsampekis. His  talk is entitled as “Matching in
graphs, circuits and toric ideals”.


 All are most welcome to attend.



Please find the  more detailed announcement below.

Sincerely

Burcu Silindir Yantır
İzmir University of Economics

Department of Mathematics



*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.
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