Description:

Title: Classification of highly-connected manifolds

Abstract: The problem of classifying smooth, closed, highly-connected

n-manifolds (for n \geq 5) up to diffeomorphism has a long history in

the study of geometric topology—in the 1950s, Milnor's study of this

problem led to his discovery of exotic spheres. In this talk, I will

survey this classical problem and discuss its solution, which builds

on the work of many people, including Wall, Stolz, and Mahowald. This solution,

obtained in joint works with Burklund, Hahn and Zhang, relies on

modern techniques in the higher algebra of E_\infty-rings. Time

permitting, I will also explain how to generalize this classification

from highly-connected manifolds to the wider class of

metastably-connected manifolds.