Université McMaster, 5 - 8 décembre 2014
More recently, there have been attempts to make connections between topological monodromy in classical mechanics, and quantum phenomena, specifically in energy levels of particles and molecules (see work by Vu Ngoc, Sadovskii and others). In this talk I will give a brief introduction to topological monodromy of integrable systems, and present a completely integrable system on $S^2\times S^2\times S^2$ which has non-trivial topological monodromy, as well as some relation to recent research in quantum physics (see the preprint arXiv:1411.7063).
This classification has a nice combinatorial description, in terms of subdiagrams of a certain Coxeter diagram. This suggests the existence of a close relationship between two compactifications of the moduli space of K3 surfaces of degree two: one defined by the minimal model program and the other given as a toric blow-up of the Baily-Borel compactification defined by a Coxeter diagram.