Eigenvalue problems occupy a central role in Riemannian geometry, providing profound insights into the interplay between geometry and analysis. At their core, these problems involve the study of ...

Biharmonic maps extend the concept of harmonic maps by exploring critical points of higher order energy functionals. In Riemannian geometry, while harmonic maps minimise the classical energy ...

LOS ALAMOS, N.M., August 10, 2022—A new study corrects an important error in the 3D mathematical space developed by the Nobel Prize–winning physicist Erwin ...

While artificial intelligence (AI) has made remarkable achievements in domains like image recognition and natural language processing, it encounters fundamental challenges when trying to deal with ...

Quantum Riemannian geometry is a generalisation of geometry that allows coordinates to be noncommutative. The project will focus on a particular approach to this [1] in which differential forms are ...

On a flight from New York City to Berlin, the route map might look a little curious: the shortest path between these two cities is surely a straight line, and yet the flight path curves distinctly, ...

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 ...