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Geometry and Topology Seminar

Friday, October 21, 2022
4:00pm to 5:00pm
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Linde Hall 187
Geography problem in 4 dimensional topology and Mahowald invariants
Zhouli Xu, Department of Mathematics, UCSD,

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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit