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Hyperbolic hydrodynamic limits and thermodynamic entropy solutions

We study the hydrodynamic limit of a anharmonic chain subject to boundary condition in the hyperbolic space-time scale. By suitably adding noise to the Hamiltonian dynamics the macroscopic equation is...

Sulle superfici sferiche con punti conici.

Una superficie sferica con punti conici è una varietà reale, compatta, orientata, di dimensione 2, che può essere ottenuta dall'unione disgiunta di finiti triangoli sferici convessi, identificando iso...

Alcuni risultati sul calcolo di potenziali multidimensionali

Inizialmente presenterò alcuni risultati riguardanti il calcolo di potenziali di volume basati sull' "approximate approximation" delle relative densità mediante funzioni gaussiane o funzioni ad esse c...

Operator algebraic aspects of Quantum Field Theory

La teoria algebrica dei campi quantistici è una teoria assiomatica utile a costruire e studiare proprietà di modelli quantistico-relativistici definita da Haag e Kastler nel 1964. In questa analisi si...

Some prescribed curvature problems in differential geometry

An important class of problems in geometric analysis consists in deforming the metric of a surface (or higher-dimensional manifold) in suitable ways, so that the new metric has a prescribed value of c...

Deformations of varieties of general type

We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera....

Where geometry meets dynamics: groups, entropy and Hausdorff dimension

I will discuss geometric and dynamical properties of actions of discrete groups on Riemannian symmetric spaces. I will highlight some aspects of the interplay between geometry and dynamics, and presen...

Segregation in predator-prey models and the emergence of territoriality

I report here on a series of joint works with Alessandro Zilio (Université de Paris) about systems of competing predators interacting with a single prey. We focus on the analysis of stationary states,...

On extension of twisted canonical forms defined on the central fiber of a Kähler family

We will report on a joint work with J. Cao. Our main result establishes the extension of twisted canonical forms defined on an infinitesimal neighborhood of the central fiber of a Kahler family under ...

Dalle trasformazioni quadratiche alle trasformazioni cremoniane

Gli sviluppi più notevoli dello studio delle trasformazioni geometriche si ebbero nella seconda metà del XIX secolo e culminarono nell’opera di Luigi Cremona sulle trasformazioni birazionali del piano...

Canonical sheaves at isolated canonical singularities

The canonical line bundle and the corresponding canonical sheaf belong to the most important geometric/analytic objects associated to a complex manifold. They play a crucial role e.g. in classificatio...

Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold

We consider the problem of finding domains that minimize the first eigenvalue of the Dirichlet Laplacian in a Riemannian manifold under volume constraint (Faber-Krahn minimizers). In the Euclidean set...