For a long time, the vortex equations and their associated self-dual field theories have provided a class of toy models in condensed matter theory and particle physics. But more recently, vortices (or their avatars such as stable pairs, holomorphic triples/chains, and quasi-maps) have also been attracting increasing interest from the mathematical community, proceeding from their very natural symplectic-geometric interpretation. In various contexts, a prominent role has been played by the moduli spaces of these objects -- they have been investigated from viewpoints such as geometric quantization, localization of supersymmetric gauge theories, geometric group theory and enumerative geometry. On the other hand, several constructions related to the notion of duality in QFT have also relied on vortices and their extensions. Our program is aimed at discussing recent research on vortex moduli (in their different guises, addressing their topology and geometry), as well as showcasing new develo...
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