Seminar Archives

Pure Maths Colloquium: On contact topology, Symplectic Field Theory and the PDE that unites them

3 December 2012 16:00 in CM221

The fields of symplectic geometry and contact geometry are often
referred to as even and odd-dimensional "cousins". While a symplectic
manifold can be viewed as the natural geometric setting for
Hamiltonian mechanics, a contact manifold is essentially the
restriction of that setting to a hypersurface of constant energy. In
this talk I will discuss some of the basic topological questions
regarding contact manifolds, and explain why these questions can be
studied using a seemingly unrelated algebraic formalism in the style
of a "topological quantum field theory". One of the main insights to
emerge recently from this connection is the fact that contact
manifolds admit varying "degrees of tightness", which give us
information on their relationships to one other and to symplectic
manifolds. I will also sketch some basics on the analytical
technology in the background of all this, a nonlinear elliptic PDE
whose solutions are called "pseudoholomorphic curves".

Contact anna.felikson@durham.ac.uk for more information