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 developments at the level of generalizations and applications.
The first week of this ICTS program will be a workshop consisting of minicourses (4 lectures each) on various themes in the study of vortex moduli spaces:
1. Vortices and symplectic duality (Mathew Bullimore, Durham University, UK)
2. Geometry of vortices on Riemann surfaces (Oscar García-Prada, ICMAT, Spain)
3. Quantization of vortices (Nuno Romão, University of Augsburg, Germany)
4. L^2 geometry of moduli spaces of vortices and lumps (Martin Speight, University of Leeds, UK)
5. Symplectic vortices and the quantum Kirwan map (Chris Woodward, Rutgers University, USA)
These lectures will be aimed at graduate students, young postdocs, and other researchers who wish to enter the field.
The second week of the program will feature research talks on various aspects of vortex moduli spaces and applications.