Geometry and Topology Seminar

The geography problem in 4 dimensional topology asks which closed simply connected 4-manifolds admit a smooth structure. After the celebrated work of Kirby-Siebenmann, Freedman, and Donaldson, the last uncharted territory of this geography question is the "11/8-Conjecture'', which states that for any smooth spin 4-manifold, the ratio of its second-Betti number and signature is least 11/8.

In this talk, I will discuss some recent progress on the "11/8-Conjecture'' by studying a problem in Pin(2)-equivariant stable homotopy theory using Mahowald invariants. This is a joint work with Mike Hopkins, Jianfeng Lin and XiaoLin Danny Shi.