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Yuguang Zhang: Lectures

September 14, 2017
TITLE: Collapsing of hyperkahler manifolds

ABSTRACT: In this talk, we study the collapsing of hyperkahler metrics on projective holomorphic symplectic manifolds along holomorphic Lagrangian fibrations. We prove that the Gromov-Hausdorff limits are compact metric spaces, which are half-dimensional special Kahler manifolds outside singular sets of real Hausdorff codimension 2.

Eirik Svanes: Lectures

September 14, 2017
TITLE: On the Coupled Moduli Space of Exceptional Holonomy Manifolds with Instanton Bundles

ABSTRACT: Recent years have seen a renaissance in the construction and study of new examples of manifolds with exceptional holonomy, instanton bundles over these spaces and their applications in physics and string theory. Due to anomalies and alpha’ corrections, the bundle often has a non-trivial back-reaction on the base geometry, and it can be important to keep this in mind when studying aspects of the solutions such as the moduli problem. These corrections are of particular importance in the context of the heterotic string, and I will review some recent work that highlights this and discuss the heterotic moduli problem in particular.

Slides of Lecture

Samson Shatashvili: Lectures

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 G_2 (or Spini7) holonomy manifolds, and corresponding mirror symmetry conjecture.

Aleksander Doan: Lectures

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.

Gao Chen: Lectures

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 G_2 and slow rate of convergence to the cone metric is constructed on a ball inside the cone over the flag manifold.

Daniel Butter: Lectures

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.

Gavin Ball: Lectures

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 G_2. 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 G_2-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.

Tommaso Pacini: Lectures

June 8, 2017
TITLE: Geometry and analysis of conifolds

Yang Li: Lectures

June 7, 2017
TITLE: A new complete Calabi-Yau metric on C3 with maximal volume growth

Alessio Corti: Lectures

June 6, 2017
TITLE: (Weak) Fano 3-folds and CHNP