There is a history of fruitful links between low-dimensional topology and number theory, going back at least to Mazur’s observation that primes in number rings can be viewed as analogues of knots in a 3-manifold. More recently, the introduction of arithmetic gauge theory by M. Kim and collaborators paves the way to further bring ideas from theoretical physics to bear on fundamental problems in number theory and arithmetic geometry.

This conference aimed to explore this exciting new direction, and the links between number theory, topology and physics in general, with a particular focus on the role played by gauge fields as a unifying framework. In doing this, we brought together experts and early career researchers in each of the areas mentioned above, with a view to fostering new collaborations and enabling participants to become acquainted with recent developments.