On the Structure of the Small Quantum Cohomology Rings of Projective Hypersurfaces

We give an explicit procedure which computes for degree $d \leq 3$ the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface $X$ as homogeneous polynomials of degree $d$ in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi-Yau hypersurfaces and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which express the structural constants of the quantum cohomology ring of $X$ as weighted homogeneous polynomial functions in the constants of the Fano hypersurface with the same degree and dimension one more. We propose some conjectures about the existence and the form of the recursive formulas for the structural constants of rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree 4 and 5.Comment: 32 pages, changed fonts, exact results on quintic rational curves are added. To appear in Commun. Math. Phy

Monotone and Consistent discretization of the Monge-Ampere operator

We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are achieved by exploiting the arithmetic structure of the discrete domain, assumed to be a two dimensional cartesian grid. The construction of our scheme is simple, but its analysis relies on original tools seldom encountered in numerical analysis, such as the geometry of two dimensional lattices, and an arithmetic structure called the Stern-Brocot tree. Numerical experiments illustrate the method's efficiency

La manifestación de la huella a través de los espacios narrativos : una lectura de Nanina de Germán García

La novela Nanina genera interrogantes desde su creación hasta el momento posterior a su lectura. La irregularidad de la estructura nos lleva a reflexionar acerca de lo que significó el impacto de este novedoso recurso entre los lectores de la época (1968), en el marco de un contexto social y político controvertido