Our research activities focus on the development of advanced mathematical models for the analysis of complex systems in theoretical physics, engineering, and materials science. The goal is to provide rigorous and innovative tools that support the understanding of fundamental phenomena and emerging technological applications.

A central theme concerns classical and relativistic field theories, with particular attention to alternative gravitational models that go beyond the standard paradigm. These models are applied to the study of compact objects, anisotropic dynamics, and cosmological scenarios.

The interaction between quantum mechanics and spacetime geometries is addressed through the study of quantum field theories in curved spaces. These investigations intertwine with the analysis of the mathematical foundations of quantum information, where differential geometry and abstract algebra play a key role in the formalization of computation and communication models.

Another line of research focuses on solid mechanics and the study of advanced materials. Continuous modeling techniques and variational methods are employed to describe mechanical and thermal properties, with applications in structural engineering and materials science.

Geometric techniques are also applied to the analysis and control of dynamical systemsdescribed by partial differential equations. This approach allows for tackling complex problems in simulation and engineering contexts.

The framework is completed by diffusion theory, used to model phenomena in heterogeneous media and complex systems, and computational engineering, which employs mathematical modeling to optimize the design of physical and industrial systems.

The integration of theoretical rigor and practical applications is the hallmark of the group, which promotes innovation through the dialogue between mathematics and technology.

Involved Laboratories

Laboratory of Applied Mathematics, Simulation, and Mathematical Modeling.

Representative Publications

•     Parameter estimation of fire propagation models using level set methods - A Alessandri, P Bagnerini, M Gaggero, L Mantelli, Applied Mathematical Modelling 92 (2021), 731-747.
•       Reconstructing isotropic and anisotropic cosmologies - F Esposito, S Carloni, R Cianci, S Vignolo, Physical Review D 105 (8), 084061 (2022)
•      Quantum random access codes and incompatibility of measurements - C Carmeli, T Heinosaari, A Toigo, Europhysics Letters 130 (5), 50001 (2020)
•       Quantum gravity phenomenology at the dawn of the multi-messenger era—A review - A Addazi et al, including V Vitagliano, Progress in Particle and Nuclear Physics 125 (2022), 103948
•       Spinors in polar form – L Fabbri, European Physical Journal Plus, (2021), 136(4), 354