C5

My research focuses on numerical techniques that help provide scalable computation within simulations of two-phase fluid flow problems. The efficient solution of the linear systems which arise is key to obtaining practical computation. I will motivate and discuss new methods which seek to generalise effective techniques for a single phase to the more challenging setting of two-phase flow where the governing equations have discontinuous coefficients.

A Fueter map between two hyperKaehler manifolds is a solution of a Cauchy-Riemann-type equation in the quaternionic context. In this talk I will describe relations between Fueter maps, generalized Seiberg-Witten equations, and Yang-Mills instantons on G2-manifolds (so called G2-instantons).

Abstract: Ricci solitons are genralizations of Einstein metrics which have become subject of much interest over the last decade. In this talk I will give a basic introduction to these metrics and discuss how to reformulate the Ricci soliton equation as a Hamiltonian system assuming some symmetry conditions. Using this approach we will construct explicit solutions to the soliton equation for manifolds of dimension 5.