I've reached the cosmology part of my General Relativity (GR) course, and one of the early points that comes up is my traditional rant against confusing three very distinct concepts when thinking ...

Hyperplane arrangements lie at the confluence of algebraic geometry, topology and combinatorics, offering a multifaceted arena in which algebraic methods illuminate topological invariants and vice ...

In the computer vision field of object detection, deep learning models are trained to identify objects of interest within an image of a scene. For example, such models can be trained to detect viruses ...

The cosmos may have something in common with a doughnut. In addition to their fried, sugary goodness, doughnuts are known for their shape, or in mathematical terms, their topology. In a universe with ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

When students are genuinely curious about new concepts and ideas, they develop their own study skills, says Pekka Pankka, professor and teacher in the specialization. Geometry, Algebra, and Topology ...

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 ...

In this course we will consider the structure of (infinite) groups. For this, we will study actions of groups on interesting topological and metric spaces. The geometry of these spaces can be used to ...

Soft matter is a truly interdisciplinary field of study encompassing an ever broadening array of subjects, ranging from elasticity, complex fluids, and metamaterials, to physics of living matter and ...