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BIRS Workshop Lecture Videos

$S^1$ invariant Laplacian flow Fowdar, Udhav


The Laplacian flow is an evolution equation of closed $G_2$-structures arising as the gradient flow of the so-called Hitchin volume functional. In this talk, we shall consider the flow of those $G_2$ structures admitting $S^1$ symmetry and derive explicitly the evolution equations of the $\mathrm{SU}(3)$-structure on the quotient manifold together with a connection 1-form. We describe these equations in a couple of examples and mention some partial results of ongoing work.

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