Name: Apostolos Thoma Title: On the bounds of the binomial arithmetical rank for simplicial toric varieties. Abstract: This is a joint work with Margherita Barile and Marcel Morales. Let $V$ be a simplicial toric variety. The ideal of a toric variety is a prime binomial ideal. The binomial arithmetical rank of a binomial ideal $I$ is the smallest integer $s$ for which there exist binomials $f_1, \dots , f_s$ in $I$ such that $rad(I)=rad(f_1, \dots , f_s)$. The binomial arithmetical rank is an upper bound for the arithmetical rank of a binomial ideal. The talk will discuss about upper bounds for the binomial arithmetical rank of the ideals of simplicial toric varieties.