210309 Mingcong Zeng

March 9, 2021

Title: From exotic spheres to equivariant homotopy

Speaker: Mingcong Zeng

In 1956, Milnor discovered that there are several smooth structures on the 7-spheres that are not diffeomorphic to the standard one. In 1963, Kervaire and Milnor provided a method of counting the number of smooth structures on spheres of dimension greater than 4. In this talk, I will start with their results, and talk about how this geometric problem was transformed into a problem in homotopy theory, and discuss how equivariant homotopy comes into play. Finally, I will talk about some recent results with my collaborators on equivariant homotopy and some confusing problems I am thinking about.

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