Symplectic Singularities, Supersymmetric QFT, and Geometric Representation Theory: March 31st – April 4, 2025.

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Organized by:

• Tomoyuki Arakawa (Kyoto University)
• Christopher Beem (University of Oxford)
• Antoine Bourget (IPhT Saclay),
• Thomas Creutzig (University of Alberta)
• Julius Grimminger (University of Oxford)
• Daniel Juteau (LAMFA, Université de Picardie)
• Paul Levy (Lancaster University)
• Leonardo Rastelli (Stony Brook University)
• Brandon Rayhaun (Stony Brook University)
• Alex Weekes (University of Saskatchewan)

Supersymmetric quantum field theories (SQFTs) have been intensely researched by both physicists and mathematicians for decades. For physicists, they furnish computationally and conceptually tractable models from which one may hope to extract general lessons about quantum field theory. On the other hand, supersymmetry also often equips such theories with additional structures, both algebraic and geometric, which are mathematically rich and warrant study in their own right. This event focuses on SQFTs of diverse dimension, the geometry of their moduli spaces of vacua, and the algebras formed by their supersymmetry-preserving operators, particularly when these take the form of a vertex operator algebra. The interplay between these three subjects bears fruit; a better understanding of any one of the three enriches both of the other two.

Symplectic singularities lie at the crossroads between algebraic geometry and representation theory, while from the physical perspective they arise as moduli spaces for supersymmetric quantum field theories. As such, they can be studied using tools from string theories and branes, in addition to tools from algebraic geometry, sheaf theory, and beyond. Notable examples include slices to nilpotent orbit closures and their covers, symplectic quotient singularities, slices in the affine Grassmannian, quiver varieties, and associated varieties for vertex operator algebras. In the last few years, the rigorous construction of Coulomb branches, motivated by 3d gauge theories, has opened new avenues of study, including surprising connections between singularities investigated in the context of classical integrable systems of Calogero-Moser type and moduli spaces of super(-conformal) quantum field theories. This workshop will bring together mathematicians and physicists, with symplectic singularities as a focal point, to push further these connections and aim at a global understanding, with implications for the classification of SQFTs.

This workshop is associated with the program: Supersymmetric Quantum Field Theories, Vertex Operator Algebras, and Geometry – March 17th – April 18th, 2025.