On Thursday afternoon, Eugen Varvaruca spoke on global bifurcation of gravity waves with vorticity. He first reviewed the various formulations suitable for global bifurcation theories, and settled on Bobenko’s formulation as a starting point. He introduced a new integro-differential formulation which generalizes Bobenko’s formulation to finite depth and non-zero vorticity. This formulation can be characterized as the Euler-Lagrange equation for a suitable functional. A generalization of the periodic Hilbert transform was introduced, and used to define a Dirichlet-Neumann operator of the form w –> [w]/d + C(w’) where C(.) is the generalized Hilbert transform and [.] denotes average. Real analytic bifurcation theory was used to find branching travelling waves. First local bifurcations were established in the massflux-energy (Bernoulli) plane. Then global results were established using Rabinowitz’s theorem. Several possibilities for global branches were discussed: reconnect to a trivial solution, stagnation points, singularities, but the theory has yet to discriminate which case occurs. A preprint Constantin, Strauss & Varvaruca (2014) has been posted on the arXiv. A video of the talk is available here.