Seminar | Institute of Mathematical Sciences
Time：14:00-15:00, May 22, Wednsday
Location：Room S407, IMS
Speaker: Matthew Randall, IMS
Abstract: Einstein-Weyl geometry has received renewed interest in recent years because of its connection to twistor theory and integrable PDEs. A result of Ferapontov and Kruglikov shows that various classes of second-order dispersionless PDEs define Einstein-Weyl structures on the conformal metric given by their principal symbols. As an overdetermined system of PDEs the Einstein-Weyl equation asks for a Weyl connection or a 1-form that preserves the conformal metric and that the symmetrised Ricci tensor of the Weyl connection be proportional to the metric. It can be seen that this equation naturally generalises the conformal-to-Einstein condition. I will review and talk more about the Einstein-Weyl equation in the context of conformal differential geometry.