We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group GC, sometimes in multiple ways. In the background of aâ€¦ (More)

We study a family of equations defined on the space of tensor densities of weight Î» on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to theâ€¦ (More)

We explore numerically different aspects of periodic traveling-wave solutions of the Camassaâ€“Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions andâ€¦ (More)

The Hunterâ€“Saxton equation is the Euler equation for the geodesic flow on the quotient space of the infinite-dimensional group of orientation preserving diffeomorphisms of the unit circle modulo theâ€¦ (More)

We consider an integrable generalization of the nonlinear SchrÃ¶dinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLSâ€¦ (More)

A supersymmetric extension of the Hunter-Saxton equation is constructed. We present its bi-Hamiltonian structure and show that it arises geometrically as a geodesic equation on the space ofâ€¦ (More)

We study the geometry of the space of densities Dens(M), which is the quotient space Diff(M)/DiffÎ¼(M) of the diffeomorphism group of a compact manifold M by the subgroup of volume-preservingâ€¦ (More)