Complex geometry investigates the properties and structures inherent in complex manifolds, while hyperbolicity imposes stringent restrictions on the behaviour of holomorphic maps. Together, these ...

Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

To a nonmathematician, having the letter "i" represent a number that does not quite exist and is "imaginary" can be hard to wrap your head around. If you open your mind to this way of thinking, ...

Our February Insights puzzle sent readers on a treasure hunt based on complex numbers. First we provided a bit of a primer, demonstrating that complex numbers (expressions of the form a + bi, where ...

Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

In science and engineering, it's unusual for innovation to come in one fell swoop. It's more often a painstaking plod through ...

Masaki Kashiwara received the honor, often regarded as the Nobel Prize in mathematics, for work that combined different mathematical fields to solve challenging problems. By Kenneth Chang Masaki ...