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We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in ref. [1] does not trivially reduce to f(R) models. It will also produce an example of theory that on-shell endowes spacetime with a non-trivial Weyl geometry where the connection is not induced by the metric structure (though it is compatible with it in the sense of Ehlers-Pirani-Schild; see ref. [2])., Some refs added

Different notions of mechanical energy and conservation laws are considered and discussed from the viewpoint of transformation laws with respect to changes of reference. Here, in particular, we shall consider and investigate the behavior of suitable conservation laws in non-inertial frames.

We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Noether currents and superpotentials are computed so that results are easily compared with the well-known results in dimension 3. Finally we use this covariant formulation of Chern-Simons theories to investigate their relation with topological BF theories.

In the framework of Digital Art applied to Scientific Visualization we have realized a short video together with an interactive multimedia aimed at visualizing and diffusing the main concepts of Special Relativity. This note makes a short presentation of it.

Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and the parametrization are gauge covariant and some further conditions are satisfied in order to formulate a Nöther theorem that links horizontal and gauge symmetries to the relative conservation laws (generalizing what Fernández, García and Rodrigo did in some recent papers). The case of vakonomic constraints in field theory is also studied within the framework of parametrized variational problems, defining and comparing two different concepts of criticality of a section, one arising directly from the vakonomic schema, the other making use of an adapted parametrization. The general theory is then applied to the case of hydrodynamics of a charged fluid coupled with its gravitational and electromagnetic field. A variational formulation including conserved currents and superpotentials is given that turns out to be computationally much easier than the standard one.

It is known that superpotentials of so-called higher-order theories of gravitation and Einstein theories with a cosmological constant are different in the "Palatini" formulation. However, these theories share a number of solutions, the energy of which should be defined out of superpotentials. We shall check that using augmented variational principles, recently introduced by us, the energy of a solution is defined regardless of the theory, and hence regardless of the superpotential used.

We investigate the covariant formulation of Chern–Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Nöther currents and superpotentials are computed so that results are easily compared with the well-known results in dimension 3. Finally we use this covariant formulation of Chern–Simons theories to investigate their relation with topological BF theories.

We shall review some results about the globality of Chern–Simons theory in any odd dimension. The relation between Chern–Simons theories and some recent results about conservation laws are also considered in detail.

We review the classical notion of spin structure on a (pseudo)-Rienannian manifold and appropriately extend it to be applied to manifolds without any a priori fixed metric structure. The relation with soldering forms is discussed in detail and so-called Ashtekar variables for four-dimensional Euclidean GR are introduced as a leading application.

We review the definition by Perlick of standard clocks in a Weyl geometry and show how a congruence of clocks can be used to fix the conformal gauge in the EPS framework. Examples are discussed in details., Comment: 14 pages, 4 figure

Mauro Francaviglia was born in Torino, on 22nd June 1953 and passed away in Cosenza, on 24th June 2013. He graduated, magna cum laude, in Mathematics at the University of Torino in 1975. He held the position of Full Professor of Mathematical Physics at the University of Torino since 1980, when he was 27 years old. He was considered an extremely valid researcher and he was one of the best Italian Mathematical Physicists of his generation. Mauro started his research activity in General Relativity, as a classical relativist, and his scientific interests covered a wide range of topics, including the application of Differential Geometry in Mathematical Physics, Classical Mechanics, Field Theories, Calculus of Variations, Symmetries and Conservation Laws, Quantization, Thermodynamics and, in late years, Extended Theories of Gravitation. Author of over 250 papers, three monographs and 11 encyclopedia long entries, Editor of 19 volumes of Proceedings and Director of two CIME courses. He organized 20 national and international conferences, among which several national conferences in General Relativity and the World Conference GR14 (Florence, 1995). He has been the Director of several national and international research projects and he held over 300 invited lectures at various institutions in Italy and abroad. He supervised several successful Ph.D. students. Mauro has been a member of the Scientific Council of GNFM-CNR (1980–1996), a co-founder (1984) and Managing Editor of “Journal of Geometry and Physics”, a co-founder (1990) and President (1990–1996 and 2008–2012) of the Italian Society for General Relativity and Gravitation (SIGRAV). He was a life member of the