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 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 ...

Our perception of our environment can deceive us. A map, although flat, effectively guides us through a space that, in reality, is not flat at all. We live on a giant sphere, a reality that goes ...

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 ...

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 ...

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 ...

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 ...