Algebraic groups and their representations lie at the heart of modern mathematics, forming a bridge between abstract algebraic structures and geometric intuition. The study of algebraic groups entails ...

Differential Galois theory extends the classical study of algebraic symmetries into the realm of differential equations. This area investigates the relationship between a differential equation’s ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? Representation theory transforms abstract algebra groups into things like simpler ...

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses. “I’m nearly at the end of the talk, and it’s ...

The original version of this story appeared in Quanta Magazine. Mathematics started with numbers—clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract ...

Algebra The Algebra group focusses on group theory and representation theory. Groups are algebraic structures that arise naturally throughout mathematics. They encode the symmetries in a vast range of ...