The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on June 13, 2017  at 2 p.m. in Room 478 of IMI.

A talk on:

Adiabatic Limit in Ginzburg-Landau and Seiberg-Witten Equations

will be delivered by Armen Sergeev, Steklov Mathematical Institute, Moscow.

Everybody is invited.

Abstract. We study solutions of Ginzburg-Landau equations arising in superconductivity theory. Static solutions, called otherwise vortices, are completely described by the Taubes theorem. However, it is not much known about the structure of dynamical solutions of these equations. The adiabatic limit method allows to describe the slowly moving solutions. In this limit Ginzburg-Landau equations reduce to the adiabatic equation which coincides with the Euler equation for geodesics on the space of vortices with respect to the Riemannian metric determined by the kinetic energy. An analogous adiabatic limit is used for the approximate description of solutions of the Seiberg-Witten equations on 4-dimensional symplectic manifolds. In this limit one obtains instead of geodesics the pseudoholomorphic curves while solutions of Seiberg-Witten equations reduce to the families of vortices defined in the normal planes to the limiting pseudoholomorphic curve. Such families should satisfy a nonlinear ∂ ̅-equation which can be treated as a complex analogue of the adiabatic equation