3. SFT

Problem 3.1.
Completeness of the SFT Hamiltonian system i.e. do the Hamiltonians $h_{\alpha,i}$ form a maximal commuting set in $H_*(\mathcal{P})?$
In particular, in the case of symplectic mapping tori, use the relation to Floer theory of the underlying symplectomorphism to find appropriate generalizations of Frobenius manifolds and bihamiltonian structures. Does there exist a flatness equation on SFT homology? Study these questions for the example of local SFT. 
Problem 3.3.
Computation of the commuting Hamiltonians for subcritical Steinfillable manifolds using Legendrian SFT.
Particular example: \[ M=\left\{\left\{f(x_1,..,x_n)=\epsilon\neq 0\right\}\cap S^{2n+1}\right\} \] where $f(x_1,..,x_n)$ is a weighted homogenous polynomial.
Cite this as: AimPL: Integrable systems in GromovWitten and symplectic field theory, available at http://aimpl.org/gwsymplectic.