Home » Articles posted by Victoria Hain

# Author Archives: Victoria Hain

## Lectures: Du Pei

- 9/27/2020: Branes in moduli spaces of Higgs bundles, II

### October 27, 2020

TITLE: Branes in moduli spaces of Higgs bundles, II

ABSTRACT:

Slides of Lecture

## Lectures: Craig Lawrie

- 10/29/2020: G2, Spin(7) BPS Equations and T-branes

### October 29, 2020

TITLE: G2, Spin(7) BPS Equations and T-branes

ABSTRACT:

Slides of Lecture

## Lectures: Laura Fredrickson

- 10/27/2020: Branes in the moduli spaces of Higgs bundles, I

### October 27, 2020

TITLE: Branes in the moduli spaces of Higgs bundles, I

ABSTRACT:

Slides of Lecture

## Lectures: Lara Anderson

- 10/26/2020: Higgs Bundles in String Compactifications

### October 26, 2020

TITLE: Higgs Bundles in String Compactifications

ABSTRACT:

Slides of Lecture

## Gianluca Zoccarato: Lectures

- 09/16/2020: Unification of Higgs Bundles

### September 16, 2020 (jointly with Mirjam Cvetic)

TITLE: Unification of Higgs Bundles

ABSTRACT: We introduce a program to study compactifications of M-/F-theory on spaces with G2 and Spin(7) holonomy, which results in N=1 supersymmetry in four- and three-dimensions, respectively, by studying the world-volume gauge dynamics of Higgs bundles, which are associated with higher co-dimension singularities of special holonomy spaces.

Specifically, we will consider solutions of M-theory on local geometries with Spin(7) holonomy. The local geometry is an ADE fibration over a four manifold which gives a compactification of 7d supersymmetric Yang-Mills theory on Spin(7) manifold. The configurations of this system are controlled by a Higgs bundle on the four manifold. This Higgs bundle, which we will call the Spin(7) system, has the remarkable property of unifying other known Higgs bundles. We will show how solutions of other known Higgs bundles fit in the Spin(7) system and show how it is possible to use the Spin(7) system to create interpolating solutions between different Higgs bundles.

## Justin Sawon: Lectures

### Recorded June 2020

TITLE: Singular fibres of holomorphic Lagrangian fibrations

ABSTRACT: Fibrations on compact holomorphic symplectic manifolds are Lagrangian: their fibres must be Lagrangian with respect to the holomorphic symplectic structure. Moreover, the general fibre must be an abelian variety and singular fibres must occur in codimension one. In this talk I will survey results of Matsushita, Hwang-Oguiso, Christian Lehn, and myself that describe the structure of the singular fibres that can occur in these Lagrangian fibrations.

Slides of Lecture

## Antoine Bourget: Lectures

### Recorded June 2020

TITLE: Hasse diagrams for Symplectic Singularities via Magnetic Quivers

ABSTRACT:

In this lecture I review the construction of a finite Hasse diagram encoding the structure of singularities and symplectic leaves in conic symplectic singularities. This construction uses the concept of magnetic quiver, which is a combinatorial description of certain conic symplectic singularities, and the algorithm known as “quiver subtraction”. I then show how this can be used to gain insight about these spaces, and how this is connected to various effects in classical and quantum physics (Higgs mechanism, structure of the chiral ring, moduli space of strongly coupled SCFTs in 5 and 6 dimensions).

Slides of Lecture

## Roger Bielawski: Lectures

### Recorded June 2020

TITLE: Twistor spaces and hyperkahler metrics

ABSTRACT: I discuss several questions about twistor spaces of hyperkaehler manifolds:

multiple components of the Kodaira moduli space of sections; differential

geometry of spaces of sections which include sections with “wrong” normal

bundle; and (pseudo-)hyperkaehler metrics arising on Hilbert schemes of higher

degrees curves in a twistor space.

On this last topic, in addition to older results, I discuss the current project

with Lorenzo Foscolo, where we construct (presumably QALF) hyperkaehler manifolds

from W-invariant hypertoric varieties. We suggest that a subclass of these

corresponds precisely to the Coulomb branches of 3-dimensional N=4 SUSY gauge theories.

Slides of Lecture

## Claire Voisin: Lectures

- Recorded June 2020: Hodge theory and the topology of hyper-Kähler manifolds: an introduction
- 06/03/2020: Polarized variations of Hodge structures of hyper-Kähler type

### Recorded June 2020

TITLE: Hodge theory and the topology of hyper-Kähler manifolds: an introduction

ABSTRACT: After a short discussion of hyper-Kähler manifolds in the Riemannian and complex geometry contexts,

I discuss the general topological properties of hyper-Kähler

manifolds obtained from the local study of the period map. At the end of the talk, I start discussing

hyper-Kähler manifolds in the algebraic geometry setting, which will be the subject of the second lecture.

**The audience for this lecture is encouraged to download the slides and to follow
along in the slides while watching the video.**

### June 3, 2020

TITLE: Polarized variations of Hodge structures of hyper-Kähler type

ABSTRACT: Like for abelian varieties and complex tori, the theory of projective hyper-Kähler manifolds is very different from the theory of general Kähler ones. The former is related via the period map and Torelli theorem to the study of certain quotients of bounded Hermitian symmetric domains by arithmetic groups. I will discuss various results concerning these moduli spaces and constructions of hyper-Kähler manifolds via algebraic geometry.