MSI Friends and Alumni: Soap films in curved space

Professor Ben Andrews will be presenting a special lecture for MSI's Alumni, friends and colleagues. The presentation will be followed by drinks, hors-d’oeuvres and a chance to meet and chat with the speaker and other members of the MSI. 

Attendance at these special lectures is by invitation only, so if you would like to attend, please register as a friend of MSI to receive your invitation.


The beautiful shapes formed by soap films are modelled mathematically as 'minimal surfaces', defined by the fact that the normal curvatures of the surface along two orthogonal tangent directions are equal and opposite (so that the net force of surface tension is zero at each point).  Minimal surfaces have a rich and beautiful theory and have been a driving force in the development of many mathematical ideas over several centuries.  In recent decades they have appeared in a fascinating way in investigations of the topology of curves spaces, notably in Perelman's proof of the Poincare and geometrization conjectures on the topology of three dimensional spaces.

In this talk I will present selected highlights of minimal surface theory, and then discuss what happens when we consider minimal surfaces in the simplest possible 'curved space', the three-dimensional sphere.  I will describe how to visualise the geometry of this space, and how to construct families of minimal surfaces lying inside it.  At the end I will mention two recent breakthroughs concerning minimal surfaces in the three-dimensional sphere:  The proofs of the Willmore conjecture and the Lawson conjecture, and I will give a sketch of how the latter was proved.

About the Speaker

Ben Andrews is a Professor at the Mathematical Sciences Institute at ANU, and works on differential geometry, particularly involving applications of partial differential equations.  He received widespread recognition for his prediction that the Rolling Stones would eventually fade away and become more and more spherical, and was awarded the medal of the Australian Mathematical Society in 2003.  He is a fellow of the Australian Mathematical Society, and was elected one of the inaugural fellows of the American Mathematical Society in 2012.  He was elected a fellow of the Australian Academy of Sciences in 2013.