### Seminar in the framework of the PDE Afternoon

 12.12.2017 Type seminar Time 15:00 - 15:45 Place University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz, 1, Vienna (map) Room From 15:00 to 15:45: Hörsaal 2 (ground floor) - from 16:00 to 17:00: WPI Seminarraum (8th floor) Speaker Lucia De Luca (SISSA, Italy) Title Variational analysis for dipoles of topological singularities in two dimensions Abstract We present two continuous models for the study of topological singularities in 2D: the core-radius approach and the Ginzburg-Landau theory. It is well known that - at zero temperature and under suitable regimes - the energies associated to these models tend to concentrate, as the length scale parameter $\varepsilon$ goes to zero, around a finite number of points, the so-called vortices. We focus on low energy regimes that prevent the formation of vortices in the limit as $\varepsilon$ tends to zero, but that are compatible (for positive $\varepsilon$) with configurations of short (in terms of $\varepsilon$) dipoles, and more in general with short clusters of vortices having zero average. By using a $\Gamma$-convergence approach, we provide a quantitative analysis of the energy induced by such configurations on a continuous range of length scales. Joint work with M. Ponsiglione (Rome).