Pedro Macias Marques

On polynomials with given Hilbert function and applications

Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Social infrastructure and the preservation of physical capital: equilibria and transitional dynamics

We study the mechanisms according to which social infrastructure influences the preservation of physical capital and, consequently, economic growth. The model considers that social infrastructure is a specific type of human capital, which acts in order to preserve already existing physical capital, by, e.g., reducing the incentive for rent seeking or corruption. Using an innovative methodology in economics, the Grobner bases, we study the equilibrium of our model and conclude for the existence of two feasible steady-states or of unicity according to different combinations of parameters, highlighting a trade-off between consumption and production on one hand and social infrastructure and physical capital accumulation, on the other. We also present sufficient conditions for saddle-path stability. Finally, we describe transitional dynamics and calculate welfare effects from which we show that strengthening social infrastructure increases welfare.

Monads on projective varieties

We generalise Flo{}ystads theorem on the existence of monads on the projective space to a larger set of projective varieties. We consider a variety

The dimension of cactus varieties of cubic forms

X

Computing the cactus rank of a general form

, a line bundle

Free Extensions and Jordan type

L

Cohomological characterisation of monads

on

SPLITTING CRITERIA FOR VECTOR BUNDLES ON THE SYMPLECTIC ISOTROPIC GRASSMANNIAN

X

Free extensions and Lefschetz properties, with an application to rings of relative coinvariants.

, and a base-point-free linear system of sections of

Artinian Gorenstein algebras that are free extensions over

L