The Strange Topology That Is Reshaping Physics

In the past decade, physicists have found that topology provides unique insight into the physics of materials, such as how some insulators can sneakily conduct electricity along a single-atom layer on their surfaces.

Some of these topological effects were uncovered in the 1980s, but only in the past few years have researchers begun to realize that they could be much more prevalent and bizarre than anyone expected. . . . Now, topological physics is truly exploding.

One of the biggest surprises was that quantum states could often be explained by theories that had been invented to solve completely different problems, such as reconciling gravity with quantum physics. Concepts such as Professor Ed Witten’s topological quantum-field theories, which had subsequently led to breakthroughs in pure mathematics, were now coming back to physics in unexpected places. “It was a marvellous circle of ideas,” says mathematician Michael Atiyah, past Professor in the School of Mathematics.

Read more about the interplay between topology and physics and the roles played by Institute scholars, including Hermann Weyl, past Professor in the School of Mathematics, and former Members Shiing-Shen Chern and Michael H. Freedman, in the field's theories and applications.