Jumping from high school to college-level statistics and geometry can feel like learning a new language. The concepts get ...

Scientists have solved a long-standing geometry problem by discovering the first compact Bonnet torus pair after over a ...

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 ...

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 ...

A new tutorial co-authored by University of Birmingham researcher, Dr Mingchao Liu, Assistant Professor in Mechanical Engineering, introduces a powerful and accessible approach for accurately ...