One of differential geometry’s most challenging problems has finally been solved after 150 years, with a closed surface Bonnet pair.

Dedicated differential probes are carefully designed with matched inputs, shielding, and circuitry that reject common-mode ...

A 150-year-old geometry rule has been overturned after mathematicians found two different torus surfaces with identical ...

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 ...

Abstract: This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Itô diffusions) can be defined and studied on manifolds. No knowledge is assumed of either ...

A complete, production-ready implementation of discrete differential geometry algorithms in C++ and C#, with comprehensive documentation, tests, and examples. ddg-course-companion/ ├── README.md │ ...

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg, and Haudenosaunee peoples. Our main campus is situated on the ...

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 ...

A dipole moment of positive and negative wedge disclinations—the “the other side of the coin” of a single edge dislocation indicated by the replacement of affine connections. The inverted “T” marks ...