Thibaut Langlais (Oxford) will speak in the geometry seminar at 2pm on 3rd Februrary, in the Salle des Profs, 9th floor of building NO. Thibaut’s title is “On the incompleteness of G_2-moduli spaces” and his abstract is below.
The Lie group G_2 is one of the two exceptional cases in Berger’s list of possible Riemannian holonomy groups, and G_2-metrics have remarkable geometric properties. On a compact manifold, the moduli space of metrics with holonomy G_2 is a smooth manifold and carries a natural L^2 metric. In this talk, I will give sufficient topological and geometric conditions for a 1-parameter family of G_2-manifolds to degenerate at finite distance in the moduli space, and exhibit explicit examples of G_2-manifolds with incomplete moduli space.