Differential characters and characteristic polynomial of Frobenius.
In this paper we study the formal differential Galois group of linear differential equations with coefficients in an extension of by an exponential of integral. We use results of factorization of differential operators with coefficients in such a field to give explicit generators of the Galois group. We show that we have very similar results to the case of .
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs and areequivalentif the Newton polygons of the corresponding partition functions...