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 ...

Conformal geometry examines transformations that preserve angles, revealing deep interrelations between geometry and analysis. When combined with nonlinear elliptic equations—which are characterised ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...