Analysis and Quantum Theory Group
The interaction between mathematics and quantum theories can undoubtedly be considered one of the main drivers behind the development of modern analysis. There is every reason to believe that it will continue to stimulate cutting-edge research in the near future. Topics related to quantum mechanics have seen unprecedented growth in interest, both in theory and applications. This is evidenced nationally by the dedicated section in the PNRR strategic plan and locally by the creation of a master's degree in Quantum Engineering and a master's program in Quantum Communication and Computing.
The research group "Analysis and Quantum Theory" emerged from the convergence of various interdisciplinary research lines developed by its members in recent years, with the common goal of solving mathematical problems inherent to quantum theories. Specifically, research topics range from the existence of ground states for the nonlinear Schrödinger equation to the study of differential equations in phase space (microlocal analysis). They also include models with singular interactions, isoperimetric inequalities for entropy-type functionals, mathematical aspects of information theory and quantum computation, rigorous study of quantization problems and path integrals. There are also forays into related fields such as mathematical signal analysis, inverse problems and interactions with the mathematical problems of artificial intelligence models of current interest.
The techniques employed are diverse and pertain to various areas of modern analysis, including spectral theory, harmonic and complex analysis, and the calculus of variations. Some of the results obtained in recent years have gained significant visibility and international recognition. In addition to research activities, the group is involved in organizing a growing number of cultural initiatives, including courses, seminars, and outreach events.
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