Quantisation of moduli spaces from different perspectives

The quantisation of moduli spaces is of fundamental interest for applications both in mathematics and physics. Such a quantisation has applications in diverse fields such as Chern-Simons theory and knot theory, conformal field theories, integrability (Painlev´e theory,…), gauge theory, the geometric Langlands correspondence and furthermore, it can be obtained from different perspectives and methods. The diversity of methods used as well as the different motivations for quantising such moduli spaces makes it an extraordinary ground for developing interactions between different specialities of mathematics and physics. The most recent works on these quantisation procedures seem to indicate that it is now possible to try to unify and compare these various perspectives. This workshop aims at bringing together experts on different ways of quantising these moduli spaces:

• Experts on the quantisation from a conformal field theory and separation of variables point of view;

• Experts on the quantisation using the co-adjoint method, the Poisson structure and the corresponding integrable systems;

• Experts from the geometric quantisation perspective as well as the topological recursion method;

• Experts on the resurgence properties of some of the wave functions obtained in by such a quantisation procedure.

This worksop will not only be the opportunity for these different communities to share their results but also to develop and strengthen a common language as well as understand the motivation of each other for studying such moduli spaces both from a physics and a mathematics point of view. This will allow the researchers to collaborate more easily and hopefully develop a powerful dictionary between their methods and approaches.

Schedule

Group picture