Time: 9:00 - 11:00, October 21, 2020

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: Let $G$ be a graph on the vertex set ${1,ldots, r}$ and $R = k[x_1, ldots , x_r ]$ a polynomial ring over a field $k$. In this talk, we explicitly determine two numbers $n_0$ and $n_1$ in terms of $G$ such that $ Ass(R/overline{I(G)^n}) = Ass(R/overline{I(G)^{n_0}}$ for all $n geqslant n_0$; and $ depth(R/overline{I(G)^n}) = depth(R/overline{I(G)^{n_1}}$ for all $n geqslant n_1$. Furthermore, our $n_0$ and $n_1$ are sharp.