Alexander Baker is currently in his final year of a dual degree, BSC/BA, majoring in genetics and mathematics. His main interests are studying the behaviour of dynamical systems. This ties into a great interest for modelling and understanding biological phenomena and trying to obtain deeper theoretical understanding of these systems. However, he finds any and all mathematics extremely fascinating and has taken a recent and keen interest in the field of differential geometry. In his undergraduate degree he focused on developing research skills with summer and winter projects as well as additional research courses during semester. Alexander intends to complete Honours in mathematics while pursing further studies in statistics.
The Geometry Of Homogeneous Spaces
Manifolds generalise the concept of surfaces to arbitrary dimension. Homogeneous spaces are manifolds with a large group of symmetries and can be equipped with a Riemannian metric (RM), allowing one to define geometric notions. The prescribed Ricci curvature problem (PRCP) consists in determining RMs from their Ricci curvature (RC) tensor. A. Pulemotov obtained an existence criterion for solutions to the PRCP on a class of homogeneous spaces where the RC is positive definite. This project aims to consider this work, better understand the geometry of homogeneous spaces, and examine changes that occur if the curvature is not positive definite.