**BILKENT **

**ALGEBRA SEMINAR**

**"Bouquet Algebra of **

**Toric Ideals"**

By

# MARIUS VLADOIU

# (University of Bucharest)

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**Abstract: **To
any toric ideal (encoded by an integer matrix A) we associate a matroid structure called the bouquet graph of A, and
introduce another toric ideal called the bouquet ideal of A, which captures the
essential combinatorics of the initial toric
ideal. The new bouquet framework allows us to answer some open questions
about toric ideals. For example, we provide a
characterization of toric ideals forwhich the
following sets are equal: the Graver basis, the universal Groebner
basis,any reduced Groebner
basis and any minimal generating set. Moreover, we show that toric ideals of hypergraphs encode all toric ideals.

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**Date: ****Monday, March 30, 2015**

**Time: ****10.40-11.30**

**Place: ****Mathematics Seminar Room,
SA-141**

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**All are most cordially invited.**

Tea and biscuits: before the seminar