17 feb 2021 -- 17:00 [open in google calendar]
Dipartimento di Matematica di Pisa online
Let N be a smooth, compact, connected submanifold of a Euclidean space. We are interested in vector-valued Sobolev maps u that take their values 'close' to the manifold N - and the 'closeness' is measured, e.g., in an integral sense. For instance, u may be a Sobolev approximation of an N-valued map with singularities. Our goal is to define the `set of topological singularities' of such a map u. In some cases, this task can be accomplished by considering the distributional Jacobian of u. In this talk, instead, we will describe a different approach, based on flat chains. As an application, we will state a Gamma-convergence result for generalised Ginzburg-Landau functionals. The talk is based on a joint work with Giandomenico Orlandi (Verona).