Luz Roncal Gómez (Logroño, 1981), is a researcher employed at the Basque Center for Applied Mathematics. Her activity is focused on Harmonic Analysis and Partial Differential Equations (PDEs).
Her project will continue her collaboration with the international expert in PDEs Sundaram Thangavelu, of the Indian Institute of Sciences of Bangalore, India, focused on equations that model the behavior of quantum mechanical N-particle systems.
There is growing interest in the study of non-linear PDEs with fractional operators, as they present challenges in applications such as fluid mechanics and financial mathematics. However, they tend to be studied in Euclidean space.
What is new about this project is that it analyzes these challenges in the context of the Heisenberg group and other more abstract groups. This approach has not been explored to a great extent but it is interesting due to the role of this group in quantum mechanics.