Algebraic topology and homotopy theory constitute central areas of contemporary mathematics, exploring spaces through algebraic invariants and continuous deformations. Techniques in this field ...

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 ...

To many in the United States, advanced forms of mathematics are a terrifying maze of numbers, symbols, graphs, and hypotheticals that render our world more complex than simple observations would ...

Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF. §14.2 Algebraic Topology. Topology is generally introduced as I described it in §AG.6, ...

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 Earth's climate system seems to have shifted abruptly between colder and warmer modes in the past. Do we risk the same today from anthropogenic climate change? Frankly, climate models cannot ...

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 ...

The geometry and topology group at UB is traditionally strong in research and mentoring. Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group ...

Kevin Knudson does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

The spectrum of the canonical operator in the noncommutative 2-torus Tθ depending on the parameter θ ∈ [0,1] © Douglas Hofstadter's butterfly. Licensed under ...