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Special Holonomy and Branes (AIM workshop)
The collaboration cosponsored a workshop with the American Institute of Mathematics (AIM) on Special Holonomy and Branes on October 2630 2020. The workshop was organized by Sergei Gukov, Rafe Mazzeo, and Sakura ShaferNameki.
The workshop featured extensive discussions as well as lectures; we have preserved the lectures on this website. The entire conference was held online.
The lecture schedule was as follows. (All times are given in California time.)
Timetable:
MON 26 OCTOBER 
TUE 27 OCTOBER 
WED 28 OCTOBER 
THU 29 OCTOBER 
FRI 30 OCTOBER 

08:0009:30 (PDT) 
L. Anderson/ A. Braun 
L. Fredrickson/ D. Pei 
L. Foscolo  C. Lawrie  T. Walpuski 
12:3014:00 (PDT) 
D. Morrison/ J. Lotay 
A. Haydys/ J. Sparks 
R. Barbosa 
Speakers:
The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).
 Lara Anderson (Virginia Tech), Higgs Bundles in String Compactifications
 Rodrigo Barbosa (Simons Center for Geometry and Physics, Stony Brook), Coassociative ALE Fibrations and Spectral Covers of Riemannian Higgs Bundles
 Andreas Braun (Durham University), Higgs Bundles & Exceptional Holonomy
 Lorenzo Foscolo (University College London), QALF hyperkähler spaces
 Laura Fredrickson (University of Oregon), Branes in the moduli spaces of Higgs bundles, I
 Andriy Haydys (University of Freiburg), Special Kähler and related geometries
 Craig Lawrie (University of Pennsylvania), G2, Spin(7) BPS Equations and Tbranes
 Jason D. Lotay (Oxford University), Special holonomy and branes: observations and themes
 David R. Morrison (UC Santa Barbara), Nonabelian Gauge Symmetry in String Theory and its Cousins, including an Introduction to Branes
 Du Pei (Harvard University), Branes in moduli spaces of Higgs bundles, II
 James Sparks (Oxford University), GK geometry
 Thomas Walpuski (Humboldt Universität zu Berlin), Problems with counting G2–instantons and associatives, and generalized Seiberg–Witten equations
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 Tbranes
October 29, 2020
TITLE: G2, Spin(7) BPS Equations and Tbranes
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/Ftheory on spaces with G2 and Spin(7) holonomy, which results in N=1 supersymmetry in four and threedimensions, respectively, by studying the worldvolume gauge dynamics of Higgs bundles, which are associated with higher codimension singularities of special holonomy spaces.
Specifically, we will consider solutions of Mtheory 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 YangMills 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, HwangOguiso, 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 Winvariant hypertoric varieties. We suggest that a subclass of these
corresponds precisely to the Coulomb branches of 3dimensional N=4 SUSY gauge theories.
Slides of Lecture