Moduli spaces of symplectic vortices, well known to particle and condensed-matter physicists since the 1970s, have experienced a substantial revival over the last twenty years. This has been motivated, on one hand, by the extension of the vortex equations from linear to nonlinear targets, in a framework that replicates Gromov-Witten theory to the context of Hamiltonian spaces — where vortices become an equivariant analogue of pseudoholomorphic curves enhanced by gauge theory. On the other hand, the geometry and topology of these moduli spaces have been investigated from new viewpoints (e.g. geometric quantization, localization of supersymmetric gauge theories, geometric group theory, algebraic stacks, discrete mathematics), shedding new light both on their physical underpinnings and on sometimes unexpected links to well-established areas of mathematical research.
This workshop will be focused on various strategies to describe these moduli spaces, including their intrinsic geometry and topology, as well as on their relations to various areas of physics (e.g. gauged sigma-models with or without supersymmetry, field theory dynamics, statistical mechanics, quantization, dualities in QFT) and mathematics — with recent developments connecting to topics such as elliptic boundary value problems on surfaces, Gromov-Witten theory and moduli of curves, the theory of surface braids, topology of moduli spaces of Higgs bundles, or Floer homology.
The contributed talks will cluster around three main themes: (1) Relationship of symplectic vortices to other settings in gauge theory; (2) Topology and L^2 geometry of vortex moduli spaces; (3) Vortices and equivariant Gromov-Witten theory.