Singularity theory in differential geometry investigates points or loci at which smooth structures—such as maps, immersions or submanifolds—degenerate. At these singular points the Jacobian vanishes ...

Crystals may seem flawless, but deep inside they contain tiny structural imperfections that dramatically influence their strength and behavior. Researchers from The University of Osaka have used the ...

Differential geometry studies smooth shapes and spaces known as manifolds, using tools such as tangent spaces, curvature and connections to describe their local and global properties.

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 ...

I work in differential geometry and the application of geometry to the study of partial differential equations. Specifically, my work has focused on conservation laws, Backlund transformations, ...