Einstein metrics on Homogeneous Superspaces

Thursday, 31-Oct-2024 

Abstract

The notion of a supermanifold generalises the concept of a manifold in classical geometry by exploiting the idea of supersymmetry from theoretical physics. Supermanifolds have become an integral part of quantum field theory and arisen in other areas. In this talk, we will first discuss some of the main objectives of Riemannian geometry, particularly the construction of Einstein metrics, and survey the mathematical tools used to achieve these objectives. Subsequently, we will explain how analogues of Einstein metrics can be produced on supermanifolds and how the super setting challenges the intuition provided by the classical theory. Our focus will be on constructions involving homogeneous superspaces, which one may think of as supermanifolds with symmetries. Joint work with Yang Zhang, Mark Gould and Jorgen Rasmussen (all at the University of Queensland).