The homological singularities of maps in trace spaces between manifolds

Strong density results in trace spaces of maps between manifolds

We deal with strong density results of smooth maps between two manifolds X and Y in the fractional spaces given by the traces of Sobolev maps in W .

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Rings of Singularities

This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...

On sequences of maps with finite energies in trace spaces between manifolds

We deal with mappings defined between Riemannian manifolds that belong to trace spaces of Sobolev functions. Such mappings are equipped with a natural energy, equivalent to the fractional norm. We study the class of Cartesian currents that arise as weak limits of sequences of mappings with equibounded energies. Under suitable topological assumptions on the domain and target manifolds, we prove ...

A Few Problems on Monodromy and Discriminants

The article contains several problems concerning local monodromy groups of singularities, Lyashko–Looijenga maps, integral geometry, and topology of spaces of real algebraic manifolds.