The study of computable algebraic structures lies at the intersection of algebra, computer science and complexity theory. At its core, this field investigates how abstract algebraic systems can be ...

Algebraic structures form the backbone of many modern mathematical disciplines, providing abstract frameworks that capture the essence of operations and relations. Duality theory, in this context, ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...

K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to algebraic and geometric topology to operator algebras. The idea is to associate ...

Let à denote a smooth compactification of the k-fold fiber product of the universal family A1 → M of elliptic curves with level N structure. The purpose of this ...

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 recent work by the ...

Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...