Modern Musings on Monopoles – October 20-24, 2025

Magnetic monopoles are smooth configurations of fields in nonabelian gauge theories that behave as sources of magnetic flux from a distance. They were introduced by ’t Hooft and Polyakov in independent work published 50 years ago. Shortly after, Bogomol’nyi realised that, for a certain coupling, these objects satisfy first-oder PDEs in three dimensions (whose first solution was written down, even before this discovery, by Prasad and Sommerfield), reminiscent of the (anti)self-duality equations of four-dimensional Yang–Mills theory. Within ten years, a remarkable body of work established (among many other things) various aspects of the integrability of the Bogomol’nyi equations, the existence of multimonopoles, as well as the first important results on the geometry of their moduli spaces, including the computation of the hyperkähler metric on the space of centred 2-monopoles by Atiyah and Hitchin. These findings have been generalized and refined in many ways over the years, with monopoles playing a pivotal role in formulating key concepts in modern theoretical physics (e.g. as one of the main ingredients of electric-magnetic duality in QFT) as well as inspiring important developments in pure mathematics (such as BPS invariants).

Beyond its major value as a story of success in mathematical physics, this subject has maintained considerable vitality — and has been enjoying a clear renaissance in the last few years. With this workshop, we intend to celebrate the 50th anniversary of magnetic monopoles by spotlighting various developments and insights that have emerged more recently, and which have potential to drive further fundamental research in years to come, such as:

• progress on compactification of moduli and generalized products;
• current prospects on the Sen conjectures;
• monopole moduli in higher rank for arbitrary symmetry breaking;
• revisiting the geometry of hyperbolic monopoles;
• novel viewpoints on periodic monopoles: difference modules, holomorphic Floer theory;
• updates on Coulomb branches of supersymmetric gauge theories and their hyperkähler geometry;
• the “monopolization” program for tesserons;
• approximations to the L^2 geometry of moduli spaces via topological recursion;
• analogues of magnetic monopoles in Lorentzian signature.