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 ...

Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

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 ...

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 the recent work by ...

The spectrum of the canonical operator in the noncommutative 2-torus Tθ depending on the parameter θ ∈ [0,1] © Douglas Hofstadter's butterfly. Licensed under ...

In the field of Differential Geometry we are concerned with Riemannian manifolds or more generally (inner) metric spaces. We are interested in the interplay between their curvature and global ...

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 ...