The authors prove that the singular set of a harmonic map from a smooth Riemammian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. T

Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruen

Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. I

The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They

he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generali