In this work we introduce a new set of invariants associated to the linear strands of a minimal free resolution of a Z-graded ideal I ⊆ R = k[x1, . . . , xn]. We also prove that these invariants satisfy some properties analogous to those of Lyubeznik numbers of local rings. In particular, they satisfy a consecutiveness property that we prove rst for Lyubeznik numbers. For the case of squarefree...

We revisit Stasheff’s construction of a minimal Lie-Quillen model of a simplyconnected closed manifold M using the language of infinity-algebras. This model is then used to construct a graded Lie bracket on the equivariant homology of the free loop space of M minus a point similar to the Chas-Sullivan string bracket.

We describe a software package for constructing minimal free resolutions ofGLn(Q)-equivariant graded modules M over Q[x1, . . . , xn] such that for all i, the ith syzygy module of M is generated in a single degree. We do so by describing some algorithms for manipulating polynomial representations of the general linear group GLn(Q) following ideas of Olver and Eisenbud– Fløystad–Weyman.

We investigate the minimal graded free resolutions of ideals of at most n + 1 fat points in general position in Pn. Our main theorem is that these ideals are componentwise linear. This result yields a number of corollaries, including the multiplicity conjecture of Herzog, Huneke, and Srinivasan in this case. On the computational side, using an iterated mapping cone process, we compute formulas ...

The study of Koszul algebras and their representations has accelerated significantly in the last few years. They have been used in Topology, Algebraic Geometry and Commutative Algebra and they are used more and more frequently in Representation Theory, see for instance [BGS],[GTM],[M],[MZ] and [R]. The aim of this paper is to present some of the results presented by the second author at the Lum...

in this paper, the effects of carbon nanotube (cnt) orientation and aggregation on the static behavior of functionally graded nanocomposite cylinders reinforced by cnts are investigated based on a mesh-free method. the used nanocomposites are made of the straight cnts that are embedded in an isotropic polymer as matrix. the straight cnts are oriented, randomly or aligned or local aggregated int...