# Dr. Nuno Romao: "Asymptotic L^2 geometry of nonlinear vortex moduli"

Dec 07, 2017 from 04:15 PM to 05:45 PM

LMS 4 - Raum 526 - Übungsraum

Abstract:

The vortex equations describe vacua in gauged sigma-models on a surface $\Sigma$. Their moduli spaces support interesting Kähler metrics $g_{L^2}$ which encode information about the underlying classical and quantum field theories. In the past, various aspects of these metrics have been studied for vortices in vector bundles, but much less is known about the case of nonlinear targets, i.e. vortices in more general fibre bundles.

In my talk, I will discuss the case of target $S^2$ with its usual circle action. Then the moduli spaces become noncompact, even if $\Sigma$ is taken to be compact. There is a localisation technique that gives a concrete description of $g_{L^2}$ in terms of families of elliptic PDEs on $\Sigma$. I will show how this can be used to study the asymptotic geometry close to the boundary of the moduli spaces, from which physical information can be extracted.