报 告 题 目：Quadric Ansatz for the mn-dKP Equation and related Einstein-Weyl Spaces

主 讲 人：Prim Plansangkate

单 位：泰国宋卡王子大学

时 间：3月23日18:00

ZOOM ID：210-089-8623

密 码：123456

摘 要：

We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation. For one of these generalisations, we study solutions which are constant on a central quadric. The quadric ansatz leads to a second order ODE which is equivalent to Painleve I or II for the dKP equation, but fails to pass the Painleve test in higher dimensions. The second generalisation of the dKP equation leads to a class of Einstein-Weyl structures in an arbitrary dimension, which is characterised by the existence of a parallel weighted vector field, together with further holonomy reduction. We obtain an explicit local form for a family of Einstein-Weyl spaces belonging to this class, and depending on one arbitrary function of one variable.

简 介：

Prim Plansangkate is a mathematician at Prince of Songkla University,Thailand, was a PhD student at Cambridge University, UK, under the supervision of Prof. Maciej Dunajski, and has been a postdoc at Montreal Unversity, Canada. Plansangkate's expertise is in topology, Kähler geometry, integrable KP equations and Einstein-Weyl spaces. Plansangkate has published 7 papers in Communications in Mathematical Physics, Nonlinearity, Proceedings of the Royal Society of London A, Journal of Geometry and Physics, Nonlinearity and Classical and Quantum Gravity with more than 15 citations.