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Wednesday, October 17, 2018

**Abstract:** Abstract: In this talk, I’ll construct the Atiyah-Bott-Shapiro map that relates the periodicity of Clifford algebras to the Bott periodicity of $K$-theory. From there, I will explain the Thom isomorphism theorem for $K$ ($KO$)-theory and its relations to $\mathrm{Spin}^c$ ($\mathrm{Spin}$)-structures on a vector bundle. I’ll also talk about how the ABS construction is related to the $\hat{A}$-genus if time allows.