Generalizing symplectic topology from 1 to 2 dimensions and beyond
Symplektic geometry has flourished since the 1980s as a powerful tool for studying systems of classical mechanics. When the ordinary differential equations from classical mechanics are replaced by the partial differential equations from classical field theory, another formalism is needed to study this. However, the existing formalisms lack the same powerful tools that exist in symplektic geometry.
In this dissertation, a formalism is developed in which these tools can be applied in classical field theory.
More information on the thesis.