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March 30, 2022
Wednesday, March 30
Transformation Groups Seminar
Time: 10:30
Speaker: Kumar Shukla (Western)
Title: "Applications of Localization Formula"
Room: MC 204

Abstract: We will go over some applications of the Atiyah-Bott localization formula. We will evaluate the integral of the volume form of $S^2$ as a sum over the fixed point set of the rotation action of $S^1$ on $S^2$. A more non-trivial application will be in the enumerative problem of counting number of lines in a cubic surface in $\mathbb{CP}^3$. We will explain why this problem is well-posed and then compute the number using Atiyah-Bott formula.