Titles and Abstracts

Fernando De Felice (Università degli Studi di Padova)
Time machines. A touch of imagination skimming physical reality

Abstract:
Time machines mix up future and past, memories and expectations, old and new, conclusions and forewords.
They challenge human mind making legitimate a state of confusion. Time machines are naturally implied by the violation of chronology, the latter however is a necessary but not sufficient condition to violate causality. Some solutions of Einstein equations allow for chronology violation but the very same solutions indicate the way to prevent causality violation. We shall argue how Nature assures saving the fundamental principle of causality.

Anna Fino (Università di Torino)
The Levi-Civita's parallel transport and holonomy groups

Abstract:
The parallel transport was introduced by Levi-Civita, exploring its relation with the curvature and thus developing the modern notion of holonomy.
In this talk we will review the mail properties of the parallel transport and holonomy. We will also give an overview of special or exceptional holonomy geometries, with some recent results.

Massimiliano Guzzo (Università degli Studi di Padova)
The Levi-Civita regularization: why do we care of the three-body problem?

Abstract:
There are remarkable examples in the Solar System of orbits of a small body, such as an asteroid or a comet, which cannot be approximated (shadowed) by an orbit of the Kepler problem, even for short time intervals. The symplest model where we find these orbits is the restricted three-body problem, with the seminal examples of the second species solutions, whose existence had been conjectured by Poincare', and of the complex dynamics originating at the Lagrange points L1-L2. For these orbits, the failure of perturbation theories is related to the singularities of the gravitational potential.
Levi-Civita regularization of the symplest three-body problem (planar and circular) clearly inspired the regularizations of the spatial problem which have been succesfully formulated decades after Levi-Civita, and are broadly used in contemporary researches on the three-body problem.

Giuseppe Saccomandi (Università degli Studi di Perugia)
About some contributions by Levi-Civita in Continuum Mechanics

Abstract:
The most famous contributions of Levi-Civita in the theory of Continuum Mechanics concern some issues of hydrodynamics and in particular the theory of waves and the theory of vortices. An intensive historical research activity have been devoted to these topics that has highlighted many interesting aspects also from a scientific point of view. This talk aims not only to continue analyzing some aspects of wave theory and vortex theory, but also to highlight lesser results. In particular, we want to show how Levi-Civita's theory of waves connects to a complex KdV equation and how vortex theory has a strong connection with a geometric formulation of Euler equations which in fact is of interest to many fields of the Continuum Mechanics. Finally, with a view to providing a wider picture of Levi-Civita's scientific production, we recall minor works that consider particular problems mechanical and solid and fluid mechanics.

Tilman Sauer (Johannes Gutenberg University Mainz)
The Levi-Civita connection between physics and mathematics

Abstract:
In their search for a relativistic theory of gravitation, Albert Einstein and Marcel Grossmann in 1913 drew heavily on the `absolute differential calculus' as expounded in a long paper by Gregorio Ricci-Curbastro and Tullio Levi-Civita of 1900. Einstein did not succeed in formulating a generally covariant theory at the time and instead settled on a precursor theory with field equations of restricted covariance. When he went out to defend this theory, Levi-Civita was one of the first to put his finger on it weak spot and, after an intense correspondence between Einstein and Levi-Civita in the spring of 1915, Einstein admitted that his mathematical derivation of the Einstein-Grossmann field equations was flawed. Then, after the establishment of the final theory of general relativity, the geometric interpretation of the Einstein field equations was greatly furthered by Levi-Civita's introduction of the notion of parallel displacement. Indeed, the notion of an affine connection, conceived of as an independent object in differential geometry and thus as distinct from the more familiar metric field, in the following years opened a new field of mathematical research of exploring generalized Riemannian spaces. These developments of modern differential geometry later provided an important resource for various attempts to formulate unified field theories of gravitation and electromagnetism.

Gabriele Vedovato (INFN, sezione di Padova)
The Detection of Gravitational Waves: The Era of Multi-Messenger Astronomy

Abstract:
On Sept. 14, 2015, the gravitational waves from two black holes reached Earth and resulted in the first direct observations of gravitational waves. This confirmed a major prediction of Albert Einstein’s 1915 general theory of relativity and opened an unprecedented new window onto the cosmos. In this talk, I will present an overview of what gravitational waves are, how LIGO and Virgo interferometers detected them, and what we have learned so far. I will discuss the exciting new perspectives opened after the discovery of the spectacular collision of two neutron stars viewed for the first time both as gravitational waves by interferometers and light by other telescopes on Earth and in space, resulting in a new multi-messenger astronomy.