Chiara de Fabritiis

From Canvas to Music: Mathematics as a Tool for the Composition of Jacksontime

The creation of “Jackson time” is a project which involves a composer, Davide Amodio, and a mathematician, Chiara de Fabritiis. Our common aim was to to “translate” a painting by Jackson Pollock, Summertime n. 9, into a piece of music, making use of different mathematical tools to detect the quantities needed for the composition. We were inspired by the idea that the painting itself contained some kind of inner-music, due to the fact that Pollock’s moves during the dripping on the canvas had a sort of rhythm, indeed they were often described by witnesses as a dance. This paper describes the mathematical background, in particular it illustrates both the analysis of the painting which was carried out by the two of us and the choice of the mathematical techniques applied to compute the parameters needed for the composition, which is due to the author. The reader will find a more detailed report on the composition itself in Davide Amodio’s contribution [2].

Linear Operators on Generalized Bergman Spaces

In this paper we discuss several features of Hilbert spaces of holomorphic functions on domains of Cn. We study composition and multiplication operators on generalized Bergman spaces and give results on the dynamical behaviour (i.e. cyclicity, hypercyclicity, compactness) of the first ones and on the algebraic properties of the space that the second one interprets. In particular we underline the analogies and differences between the case of bounded and unbounded domains in C and Cn.

Analytical And Geometrical Features Of De Rham And Dolbeault'S Cohomologies

AbstractThese notes offer a short presentation of de Rham cohomology on differentiable manifolds with a proof of the isomorphism between de Rham cohomology and singular cohomology. We also recall some duality results, show how Betti numbers relate to Morse theory and shortly present the relation between de Rham and Cech cohomologies with coefficients in the sheaf of real locally constant functions for de Rham cohomology.

FIXED POINTS AND UNIQUENESS OF COMPLEX GEODESICS

In this work we examine the conditions which guarantee the uniqueness of a complex geodesic whose range contains two fixed points of a holomorphic mapf of a bounded convex circular domain in itself and is contained in the fixed points set off.