Title: The Kervaire invariant
Abstract: A surprising discovery in differential topology is that homeomorphic manifolds can admit different smooth structures; moreover, it is often possible to classify exotic smooth structures by homotopy theory. The work of Kervaire and Milnor (1963) determines the exotic smooth structures on spheres of dimension ≥5 up to knowing the stable homotopy groups of spheres and the "Kervaire invariant". Hill, Hopkins and Ravenel (2016) recently determined this invariant in all dimensions except 126 using homotopy theoretic methods.
I will give an introduction to the Kervaire invariant problem with a focus on the homotopy theoretic technique applied to solve it, namely equivariant stable homotopy theory and the equivariant slice spectral sequence.
