Differential geometry is the study of smooth manifolds and the intrinsic properties of spaces that can be described locally by Euclidean geometry. Within this expansive field, singularities represent ...

The study of algebraic structures and differential geometry has evolved into a dynamic interdisciplinary field that synthesises abstract algebraic concepts with the smooth variability of geometric ...

Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner in many areas of mathematics and physics. On a differential manifold or more ...

Application of tools from differential geometry and Lie groups to problems in dynamics, controllability, and motion planning for mechanical systems, particularly with non-Euclidean configuration ...

Mathematics is one of the oldest disciplines of study. For all its antiquity, however, it is a modern, rapidly growing field. Only 70 years ago, mathematics might have been said to consist of algebra, ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...