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Antoine Bourget: Lectures

January 10, 2022
TITLE: Magnetic Quivers for Singular HyperKähler Spaces

ABSTRACT: In this talk, following the introduction of 3d N=4 Coulomb branches in Nakajima’s lecture, I present the concept of abstract magnetic quiver to describe singular hyperKähler spaces. This is motivated by the Higgs branch of supersymmetric theories realized on the world volume of branes in string theory. The magnetic quiver gives access to algebraic and geometric properties of the spaces, which include the singularity structure and a description of the coordinate ring. These techniques can in turn be applied to describe large classes of spaces, among which hyperKähler implosion spaces, as discussed by Kirwan and Dancer in the subsequent talks. 
Slides of Lecture

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