Geometry of PDEs on Manifolds and Nilpotent Lie Groups
|
Organizer(s): |
Name:
|
Affiliation:
|
Country:
|
Jyotshana Prajapat
|
University of Mumbai
|
India
|
|
|
|
|
|
|
|
|
|
Introduction:
| | The study of qualitative properties of solutions is a fundamental aspect of theory of partial differential equations. Classification of solutions plays a crucial role in proving existence results, deriving a priori estimates, establishing comparison principles, and more.
When an equation exhibits invariance under certain transformations in the ambient space, one naturally expects its solutions to share this invariance. While various techniques have been developed in Euclidean geometry to analyze such properties, extending and adapting these methods to Manifolds and Nilpotent Lie groups presents new challenges, deeply influenced by the underlying geometric structure. Many of these geometric structures arise in the study of problems in Physics, Statistical Mechanics, Biology, Chemistry to name a few and are crucial for understanding the PDEs modelling the problems in these fields.
This session aims to bring together researchers working on PDEs in the context of Riemannian and sub-Riemannian geometries, fostering discussions on recent advancements and open problems in the field.
|
|
|
|
|
|
