Time: 9:30 -- 11:00, November 20, 2024

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

Abstract: Chains of ideals in polynomial rings of varying Krull dimensions that are invariant under the action of the infinite symmetric group Sym or the semigroup Inc of increasing functions N --> N, have attracted attention of various researchers in recent years. The behaviour of minimal generating sets, Hilbert series, codimensions of such an invariant chains of homogeneous ideals is well-understood. Howerver, the behaviour of finer homological invariants like projective dimension, Castelnuovo--Mumford regularity, and depth, remains quite mysterious, even for invariant chains of monomial ideals. Combinatorially, an Inc-invariant chain of edge ideals with a fixed stablity index and fixed number of Inc-orbits can be thought of as a chain of unions of a fixed number of isoceles right triangles in R^2 with fixed lowest vertices and varying legs. We use this combinatorial description to describe recent results on the depth and regularity of Inc-invariant chains of edge ideals. This is from joint work with T.Q. Hoa, D.T. Hoang, D.V. Le and T.T. Nguyen.

Program of Special Semester on Commutative Algebra