In 2009, Hill, Hopkins and Ravenel announced a proof of non-existence of elements of Kervaire invariant one in large dimensions. This settles a problem originated from differential topology by equivariant stable homotopy theory. In this talk, we will try to explain what the main theorem of HHR is about: we start with differential topology, then talk about stable homotopy theory and end up with equivariant methods. If time permits, we will talks bit about equivariant homotopy theory following HHR.

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