We look at an important recent result exploring higher-dimensional holes in higher-dimensional spheres.

We guide you through an exciting recent breakthrough in the world of topology, involving something called the telescope conjecture.

This collection of articles explores a recent, exciting breakthrough in the field of topology.

We continue our exploration of the telescope conjecture.

The concept of homotopy is a great example of how the language of maths can make intuition precise.

Progress in pure mathematics has its own tempo. Major questions may remain open for decades, even centuries, and once an answer has been found, it can take a collaborative effort of many mathematicians in the field to check that it is correct. The New Contexts for Stable Homotopy Theory programme, held at the Institute in 2002, is a prime example of how its research programmes can benefit researchers and its lead to landmark results.