The legacy of Tullio Levi-Civita

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A scientific conference in honor of Tullio Levi-Civita, organized by the Department of Mathematics and the University of Padua.

This initiative pays tribute to a meek gentle Padua native, whose impact was not limited to mathematics but spread also to the physics of gravitation, astronomy and civil engineering.

The year 1915 was the annus mirabilis in which Levi-Civita exchanged letters with Albert Einstein. The theory of absolute differential calculus, developed by Levi-Civita and his mentor Ricci Curbastro, was used by Albert Einstein, as crucial mathematical scaffolding for General Relativity, his revolutionary theory of gravitation.
In the first relativity of modern physics, envisioned by Galileo and Newton, the bodies' trajectories are each other deflected because of instantaneous forces generated by their masses, all such objects living in an Euclidean space. Conversely, in Einstein's relativity the trajectories are nothing but geodesics -namely, paths of minimal local length- in a non-Euclidean geometry of the space-time, a geometry which in turn is shaped by the masses. The classical physicist Max Abraham asked Levi-Civita to invalidate the theory of the brilliant German physicist, but, on the contrary, Tullio was absolutely captured by the theory. Yet he found an error in its formulation: the theory was not invariant under local coordinate transformations.

A dense correspondence followed between Levi-Civita and Einstein , in which the German physicist strongly defended his equations from the meticulous observations pinpointed by Levi-Civita. A few days before Italy entered the First World War Einstein acknowledged his error. In a letter Albert expresses his heartfelt gratitude to Tullio, and the two men will be longlife connected in a sincere friendship. Soon after this mail exchange Einstein proposed a revolutionary geometrization of gravitational physics: the field generated by the mass distribution is interpreted as a curvature of space-time. Levi-Civita, sensing the universal reach of this approach, identifies its fundamental geometrical side: the notion of parallel transport in a curved space. As it turns out, the velocity of a geodesic –a curve of minimal length-evolves parallel to itself. Parallel transport has proved quite fruitful, for it would eventually become the basic idea for the theory of connections, a crucial branch of modern geometry.

Under the fascist racial laws of 1938 Tullio Levi-Civita and many other Jewish researchers are no longer allowed to work in public activities. Levi-Civita was even banned from entering the mathematical library at the University of Rome. It is the beginning of the end: he will die heartbroken in December 1941. During those years, and thanks to the love of his students, he found the strength to write his last recollection on the N-body problem in General Relativity, posthumously published. This deep, complex work is filled with new ideas and also numerical. Its predictive potential may still not be fully explored.

 

Where: Aula Magna - Palazzo Bo - via VIII Febbraio, 2 - Padova (19/2); Room 1C150 - Torre Archimede - Padova
When: February 19-20, 2018
Further information: web site