Time: 9h00, Wednesday, November 1, 2017
Location: Room semina, Floor 6th, Building A6,, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Given a simple graph G, one can associate a binomial ideal J_G, called the binomial edge ideal of G, which is generated by x_iy_j - x_jy_i, where ij is an edge of G. It is known that in(J_G), the initial ideal of J_G with respect to the lexicographic order, is a square-free monomial ideal if and only if the graph G is a closed graph. In general, the Betti numbers of J_G are less than or equal to those of in(J_G). In 2011, Herzog, Hibi and Ene conjectured that the Betti numbers of J_G and in(J_G) are equal. In this talk, we introduce the concepts necessary to understand this conjecture and we prove the conjecture for some cases. This is a joint work with Hernán de Alba Casillas.