The study of affine hypersurfaces occupies a central role in differential geometry, providing deep insights into both the intrinsic and extrinsic properties of submanifolds in affine spaces. This ...

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 ...

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 ...

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 ...

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, ...

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 ...

When students are genuinely curious about new concepts and ideas, they develop their own study skills, says Professor Pekka Pankka. Geometry, Algebra, and Topology are pure mathematics and essential ...

The geometry and topology group at UB is traditionally strong in research and mentoring. Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group ...

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 ...