# Geometry & Topology Seminar

Thursday, September 29, 2022 — 2:30 PM EDT

Izar Alonso Lorenzo, Oxford University

"Balanced SU(3)-structures and coclosed $G_2$-structures in cohomogeneity one manifolds"

When considering compactifications of heterotic string theory, systems of PDEs involving geometric structures arise. In this talk, we will describe heterotic systems in six and seven dimensions and then study the existence of the G-structures required by them in the cohomogeneity one setting. In the first part of the talk, we provide a non-existence result for balanced non-Kähler SU(3)-structures which are invariant under a cohomogeneity one action on a simply connected six-manifold. In the second part, we find a family of coclosed $G_2$-structures on certain seven-dimensional cohomogeneity one manifolds. The first part of this talk is based on a joint work with F. Salvatore.

MC 5417

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