The sixth-sphere

The sixth-sphere

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Yanir Rubinstein, Columbia University and Clay Mathematics Institute (CMI)
Fine Hall 214

Kirchhoff's problem (1947) asks whether $S^6$ is a complex manifold. We will review basic notions in complex and almost-complex geometry and discuss a bit of what is known regarding this problem, making contact with the octonions, $G_2$, Lie brackets, and curvature.