EVENT DETAILS AND ABSTRACT

Title: Telescopes, exotic spheres, and p-adic cohomology theories
Speaker: Jeremy Hahn
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

A smooth, oriented n-manifold is called a homotopy sphere if it is homeomorphic, but not necessarily diffeomorphic, to the standard n-sphere. In dimensions n>4, one often studies the group $\Theta_n$ of homotopy spheres up to orientation-preserving diffeomorphism, with group operation given by connected sum. I will introduce the telescope conjecture in stable homotopy theory, and explain how its failure gives new lower bounds on the complexity of $\Theta_n$. To disprove the telescope conjecture, we construct invariants capable of distinguishing many diffeomorphism classes of exotic spheres: interestingly, key finiteness properties of these invariants are proved using modern advances in algebraic K-theory, cyclotomic spectra, and prismatic/syntomic cohomology.