Speaker: Zhouli Xu (University of California, Los Angeles)

Title: Proof of the existence of 𝜃₆

Abstract: The Kervaire invariant problem asks in which dimensions there
exists a stably framed manifold of Kervaire invariant one. Hill–
Hopkins–Ravenel resolved this problem in all but one dimen-
sion: 126.

In this talk, I will present an overview of the proof that $h_6^2$

survives in the Adams spectral sequence, thereby resolving the
final open case of the Kervaire invariant problem. I will discuss
new techniques involved, some of which are inspired by mo-
tivic homotopy theory. This is joint work with Weinan Lin and
Guozhen Wang.