Arithmetic geometry and p-adic differential equations form a dynamic nexus where number theory, algebraic geometry and p-adic analysis converge. This interdisciplinary field investigates the solutions ...

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

The Langlands correspondence predicts a profound connection between algebra and analysis. This connection is deep and still largely conjectural. However, in recent years there has been exciting new ...