Giacomo Canevari, "A variational approach to topological defects in materials science", Dip. di Matematica, [chiamata]
Mercoledì 22 gennaio ore 14.00 in Sala Consiglio pesso il Dipartimento di Matematica Guido Castelnuovo.
Speaker: Giacomo Canevari, vincitore, ex aequo, del concorso Professore di I fascia SSD MAT/05 - CODICE CONCORSO 2024_PO comma4ter_005
Title: A variational approach to topological defects in materials science.
Abstract: Topological defects in condensed matter systems are, loosely speaking, localised structures - carrying a topological invariant - where the typical order of the system is broken. In this talk, we take a variational approach to defects by considering a (simplified) free energy functional, sharing some featur with the Ginzburg-Landau model for superconductivity and the Landau-de Gennes model for nematic liquid crystals. In a specific asymptotic regime of parameters, minimisers of the model converge manifold-valued maps with singularities. Under suitable topological assumptions on the target manifold, we will discuss the convergence of minimisers and provide a variational characterisation of the singularities that appear in the limit, in terms of measure-geometric objects. If time permits, we will briefly menti generalisations, including problems in non-Euclidean geometries or discrete models.
