August 1
(Monday) ～ August 5 (Friday), 2016
ABSTRACT
August, 1 (Mon)  August, 2 (Tue)  August, 3 (Wed)  August, 4 (Thu)  August, 5 (Fri) 
9:3010:30  Emanuela De Negri （Genova University）
"Universal Gröbner bases and CartwrightSturmfels ideals" 
By a wellknown result of BernsteinSturmfelsZelevinsky,
the maximal minors of a matrix of variables form a universal Gröbner basis.
Also for the ideal of $2$minors of the matrix of variables the universal Gröbner basis is well described by results of Sturmfels and Villareal. In this talk we generalize these facts; we consider multigraded matrices of linear forms, and find universal Gröbner bases of the ideals of maximal minors and the ideals of $2$minors. To this aim we introduce two families of multigraded ideals, which we call CartwrightSturmfels and CartwrightSturmfels$^*$. Both families are characterized by properties of their multigraded generic initial ideals. It turns out that CartwrightSturmfels ideals are radical, and that every minimal system of generators of a CartwrightSturmfels$^*$ ideal is a universal Gröbner basis. Moreover the two classes are closed under standard operations on ideals, and this allows us to prove the desired results. This is a joint work with Aldo Conca and Elisa Gorla 

10:4511:45  Sijong Kwak （KAIST）
"Characterization of ACM varieties with dlinear resolution" 
In my talk, I consider the algebraic set, not necessary irreducible, whose graded Bettti table looks to be of the special shape, i.e. property $N_{d,e}$ or property ND(d1). We can give sharp upper bounds on the graded Betti numbers and degree bound for those categories. Only ACM varieties with dlinear resolution can appear as?the boundary cases for those upper bounds. We explain basic definitions, generic initial ideal theory and projection methods for our characterization. These are the generalization of 2linear ACM varieties in clasical algebraic geometry. 