Dr Roberto D'Onofrio
Postgraduate Research Student
Academic and research departments
Mathematics at the Interface Group, School of Mathematics and Physics.About
My research project
Fluid dynamics and Monge-Ampère geometryMy research deals with Monge-Ampere equations arising in geophysical fluid models. Monge-Ampere equations have a rich geometrical theory, which is still in continuous evolution. In recent years, pseudo-Riemannian geometry has emerged as a central aspect of this theory, but many of its features remain unexplored. My project aims to bring out the role of pseudo-Riemannian geometry as a tool for predicting qualitative aspects of solutions to the underlying fluid model, especially singular behaviours.
Supervisors
My research deals with Monge-Ampere equations arising in geophysical fluid models. Monge-Ampere equations have a rich geometrical theory, which is still in continuous evolution. In recent years, pseudo-Riemannian geometry has emerged as a central aspect of this theory, but many of its features remain unexplored. My project aims to bring out the role of pseudo-Riemannian geometry as a tool for predicting qualitative aspects of solutions to the underlying fluid model, especially singular behaviours.