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Giuseppe Marmo


Giuseppe Marmo - Università degli studi di Napoli Federico II. Italy

Prof. Marmo has been full professor of physics at the University Federico II at Naples since 1986 and is currently Emeritus professor at the same University. His scientific contributions on theoretical and mathematical physics have been of enormous relevance. He has made, among others, significant contributions to the theory of non-Abelian monopoles, to the no-interaction theorem in relativistic particle dynamics, to the inverse problem in the calculus of variations and to the classical and quantum theory of bi-Hamiltonian systems. Recently he has contributed to the study of the geometrical structure of the space of quantum states in connection with the characterisation of separability and entanglement for composite systems. He has also contributed to the formulation of nonlinear coherent states for deformed oscillators and to the foundations of Quantum Tomography. Currently he is working on the geometry of Quantum Information Theory and the foundations of Quantum Mechanics following the inspiration provided by J. Schwinger's algebra of measurements. He has published more than 300 papers on these and other topics in the most prestigious specialised international journals and is a member of various editorial committees. 



The main idea in our program will consists in showing that the highly abstract language of categories, and more specifically groupoids and 2-groupoids, provide the structures underlying Schwinger's approach to Quantum Mechanics. This scientific research programme is really ambitious and pretends to develop a consistent approach to Schwinger's ideas on Quantum Mechanics and Quantum Field Theory by means of modern mathematical tools based on category theory and groupoids.  The effort to achieve the main goals of the project will involve researchers both from the Mathematics Department at the University Carlos III de Madrid (A. Ibort and collaborators) and from other universities that will come and gather at the UCIIIM as well as my current students that will join me for some periods of time during the duration of this proposal.