The transforms that are to be the sub ject of this workshop operate on moduli spaces, either of holomorphic ob jects or of gauge fields, and have been extensively developed over the past 20 years as privileged tools in the area.
The Nahm transform was initially introduced by Nahm in the early 80’s to study magnetic monopoles. It developed over the years into a duality among instantons which are invariant under the action of a subgroup of translations of R4 . On the other hand, the Fourier–Mukai transform was also introduced in the early 80’s by Mukai as a duality among sheaves on abelian varieties. In the late 80’s it was realized that both constructions are actually equivalent in certain circumstances. Another common feature is their role in mathematical physics, notably gauge theory and string theory.
The aim of this workshop is to gather together a diverse group of people working on this fairly focused but current topic. It will attract a broad variety of participants: algebraic geometers, differential geometers and mathematical physicists. The mixture of algebraic and analytic technique required by the two transforms will lead to fruitful interaction between the participants, and to solutions of some open questions in both areas.