#68 Hunting through higher dimensions with Zhouli Xu

Welcome to the latest episode of Living Proof, our podcast produced in collaboration with Plus.maths.org– you can find all the content from the collaboration here.

On May 30th 2024 seminar goers at Princeton University witnessed a thrilling moment. The mathematician Zhouli Xu of the University of California, LA, announced that, together with colleagues he had sorted out the 126th dimension. Not in general, but in regards to a problem that has taunted mathematicians since the 1960s. The problem involves strange shapes and is called the Kervaire invariant problem, after the mathematician Michel Kervaire.

In this episode, Zhouli takes us on a trip into higher dimensions, giving us a gist of what this long-standing problem is all about and retracing some of the long, and sometimes arduous, journey towards a proof. We met Zhouli when he visited the Isaac Newton institute for Mathematical Sciences (INI) in Cambridge to take part in a research programme called Equivariant homotopy theory in Context.

To find out more abut the topics discussed in this podcast see:

• Maths in a minute: Topology
• The hypersphere in four dimensions
• Telescope topology