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September 12, 2017
TITLE: G2 superconformal theories and mirror symmetry revisited
ABSTRACT: I will discuss the world-sheet supersymmetric CFTs corresponding to the sigma models with target space being (or Spini7) holonomy manifolds, and corresponding mirror symmetry conjecture.
September 12, 2017
TITLE: Fueter sections and wall-crossing in Seiberg-Witten theory
ABSTRACT: Fueter sections are solutions to a non-linear generalization of the Dirac equation on a Riemannian spin three-manifold. The goal of this talk, based on joint work in progress with Thomas Walpuski, is to explore the relationship between Fueter sections taking values in instanton moduli spaces and wall-crossing for solutions to the Seiberg-Witten equation with multiple spinors. Time permitting, I will explain how this discussion fits into the Donaldson-Segal program of counting G2-instantons.
September 13, 2017
TITLE: Rate of asymptotic convergence near isolated singularity of a G2 manifold
ABSTRACT: In this talk, a metric with holonomy contained in and slow rate of convergence to the cone metric is constructed on a ball inside the cone over the ﬂag manifold.
September 11, 2017
Eleven-Dimensional Supergravity in 4D, N=1 Superspace
ABSTRACT: We report on progress embedding 11D supergravity in 4D, N=1 superspace. The 4D action consists of two pieces: a Chern-Simons action and a Kähler term involving the Hitchin functional. We discuss the symmetries of this action. Furthermore we compare the component action with the result obtained from Kaluza-Klein reduction of 11D supergravity to four dimensions and find agreement.
September 10, 2017
TITLE: SO(4)-structures on 7-manifolds
ABSTRACT: I will talk about the geometry of SO(4)-structures on 7-manifolds, under the restriction that the SO(4)-structure induces a metric with holonomy contained in . This amounts to a condition on the torsion of the SO(4)-structure and I will describe what happens in various cases where the torsion is restricted further. Part of this description gives a characterisation of the Bryant-Salamon examples as the unique examples with torsion lying in particular subspaces. If a -manifold is foliated by associative or coassociative submanifolds, then it carries a naturally defined SO(4)-structure. I will give an interpretation of a result of Baraglia about ‘semi-flat’ coassociative fibrations in this language, and talk about the case of ‘semi-flat’ associative fibrations.