Geometric Partial Differential Equations on Lie Supergroups

This project aims to explore the foundations of supergeometry in order to understand how
classical geometric partial differential equations can be stated in the framework of
supermanifolds and more specifically, Lie supergroups. In particular, we focus on the
Einstein equation, prescribed Ricci curvature, and the Ricci flow. Time permitting, we will
begin looking into the development of techniques to solve these equations, particularly, in
the simpler settings of low-dimensional Lie supergroups.

Benjamin Kruger

University of Queensland

Benjamin Kruger is a student at the University of Queensland. Mathematically, Ben is fascinated with differential geometry. In particular, he wants to investigate how the curvature of different shapes reveals specific properties about them. Ben’s project is to study classical geometric partial differential equations in the language of supergeometry, the canvas for theories of supersymmetry from particle physics.
Outside of mathematics, Ben loves social sports including basketball and netball. In the same realm, Ben is an avid rock climber, enjoying mostly indoor bouldering.

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