 Since 2003 he is full professor at ETH Zurich and since 2009 he is the Director of the Institute for Mathematical Research at ETH.His research interests include partial differential equations in physics (liquid crystals, Bose–Einstein condensates, micromagnetics, Ginzburg–Landau theory of superconductivity, gauge theory) and differential geometry (harmonic maps between manifolds, geometric flows, minimal surfaces, the Willmore functional and Yang–Mills fields).His work focuses in particular on non-linear phenomena, formation of vortices, energy quantization and regularity issues.