Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Forthcoming seminars

You may need the following programs to see the files

Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences
June 2, 2016 16:00, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)

Adiabatic limit in the equations of field theory

A. G. Sergeev
Video records:
Flash Video 616.7 Mb
Flash Video 3,676.0 Mb
MP4 616.7 Mb

Number of views:
This page:811
Video files:264
Youtube Video:

A. G. Sergeev
Photo Gallery

Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: The notion of adiabatic limit came into mathematics from physics and in last years widely spread in differential geometry, theory of partial differential equations, topology. In our talk we shall speak about the applications of adiabatic limit construction in equations of gauge field theory.
We start from the Ginzburg-Landau equations in dimension 3=1(time)+2(space) arising in the superconductivity theory. In the adiabatic limit these equations convert into the Euler equation for geodesics on the space of vortices (static solutions of Ginzburg–Landau equations) with respect to the metric determined by the kinetic energy.
We turn next to dimension 4 and consider the adiabatic limit in Seiberg–Witten equations on 4-dimensional symplectic manifolds. In the adiabatic limit solutions of these equations converge to families of vortex solutions parameterized by points of pseudoholomorphic curves. Such families satisfy a nonlinear Cauchy–Riemann equation. So the adiabatic limit in Seiberg-Witten equations may be considered as a complex version of the same limit in Ginzburg–Landau equations. Namely, the Euler equation is replaced by the Cauchy–Riemann equation while geodesics on the space of vortices are substituted by the “complex” geodesics in vortex bundles over pseudoholomorphic curves. In other words, dimension 4 in this case may be treated as 4=2(complex time)+2(space).

SHARE: FaceBook Twitter Livejournal
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019