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About deformations of surfaces in P^3 which are singular along a line

We will report about a jont work in progress with Ciro Ciliberto about deformations to nodal surfaces of surfaces in P^3 which are double along a line....

Introduzione ai campi quadratici reali

I campi quadratici reali, dati dall'aggiunta a \(\mathbb{Q}\) della radice quadrata di un numero positivo che non sia lui stesso un quadrato, sono uno degli oggetti centrali della Teoria dei Numeri cl...

Modelling and Simulations of Collective Dynamics - Lecture 2

The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of...

Modelling and Simulations of Collective Dynamics - Lecture 1

The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of...

Differential inclusions and polycrystals

We discuss a differential inclusion arising in the context of bounding effective conductiv- ities of polycrystalline composites. The datum is a set of three positive numbers identified with a positive...

Upper Bounds for the Dimensions of Brill-Noether Loci

A celebrated theorem by Martens states that the dimension of the locus of line bundles of fixed degree \(d\) with at least \(k\) sections on a smooth, projective, irreducible curve of genus \(g\) does...

Vitruvian polygons in symplectic problems

Each angle formed by two rays with integer slopes has two basic integer invariants: its height and its width. An angle is called Vitruvian (after a Roman architect Vitruvius advocating proportions bet...

Singular analysis of a shape optimization problem arising in population dynamic

When analyzing the survival threshold for a species in population dynamics, one is led to consider the principal eigenvalue of some indefinite weighted problems in a bounded domain. The minimization o...

Time evolution of concentrated vortex rings

The motion of fluids can sometimes be effectively modeled by a finite-dimensional dynamical system. A paradigmatic example is the point vortex model, introduced by Helmholtz in a seminal paper, which ...
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