Related papers: The Buildings Gallery: visualising buildings
Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never…
Given a semisimple linear algebraic $k$-group $G$, one has a spherical building $\Delta_G$, and one can interpret the geometric realisation $\Delta_G(\mathbb R)$ of $\Delta_G$ in terms of cocharacters of $G$. The aim of this paper is to…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c,…
These lectures are an informal elementary introduction to buildings. They are written for, and by, a non-expert. The aim is to get to the definition of a building and feel that it is an entirely natural thing. To maintain the lecture style…
Data analysis often involves the comparison of complex objects. With the ever increasing amounts and complexity of data, the demand for systems to help with these comparisons is also growing. Increasingly, information visualization tools…
I have developed a code which allows images to be produced of a variety of interacting binaries for any system parameters. The resulting images are not only helpful in visualising the geometry of a given system but are also helpful in talks…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
Drawing and visualisation of molecular structures are some of the most common tasks carried out in structural glycobiology, typically using various software. In this perspective article, we outline developments in the computational tools…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…
In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…
There has been a growing adoption of computer vision tools and technologies in architectural design workflows over the past decade. Notable use cases include point cloud generation, visual content analysis, and spatial awareness for robotic…
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Example galleries are often used to teach, document, and advertise visually-focused domain-specific languages and libraries, such as those producing visualizations, diagrams, or webpages. Despite their ubiquity, there is no consensus on the…
Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…