On higher critical points in calculus of variations

Abstract: In classical mechanics, the variational principle implies the existence of a canonical closed 2-form on the space of solutions of the Euler-Lagrange equation. I will explain an origin of this 2-form via coarse geometry, and relation with the 1st cohomology with compact support of the space-time. Then I'll introduce a generalization to higher critical points. The basic example is higher Chern-Simons theory on 5-dimensional manifolds.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar