Andrew Senger, Harvard University

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 and Stolz. 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.