Geometric representation theory is a vibrant field that unites methods from algebraic geometry, category theory and homological algebra to probe the symmetries and invariants arising from algebraic ...

In the parable of the blind men and the elephant, several blind men each describe a different part of an elephant they are touching – a sharp tusk, a flexible trunk, or a broad leg – and disagree ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that ...

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 ...