Dynamics of meromorphic vector fields on the Riemann sphere

 

Abstract: The talk will offer a brief overview on the dynamics of real-time flow of rational vector fields in one complex variable on CP^1, of their bifurcations, and of the structure the moduli space. The real phase portrait is also known as the horizontal foliation of the dual meromorphic differential form, and a great deal of the theory has a natural generalization also for horizonal foliations of meromorphic quadratic differentials.