About us

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. 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.

Some of our recent research topics include:

• Existence of ground states for the nonlinear Schrödinger equation on graphs.
• Many body quantum systems.
• Analysis of models with singular interactions.
• Microlocal and phase space analysis.
• Quantization rules and pseudodifferential calculus.
• Operators and PDEs of mathematical physics.
• Isoperimetric inequalities for entropy-type functionals.
• Mathematical aspects of information theory and quantum computation.
• Rigorous study of path integrals and functional integration.

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.