A. Prof. Julie Clutterbuck
Monash University, Australia

Geometry of level sets

We consider the shape of solutions to elliptic partial differential equations. The level sets are all the points at a fixed height. The level sets are determined by the original equation, but quantitative statements about their shapes are subtle and elusive. Moreover, methods that work directly with the level sets are pervasive across geometric analysis and numerical methods. Topics covered: basic notions for level sets, including the differential geometry of level curves; uniqueness of critical points; convexity of super-level sets; selected applications.

Relevance

Those interested in partial differential equations, geometric analysis, and potentially numerical analysis.

Pre-requisites

  • Assumed knowledge:
    • Real analysis
    • Introduction to partial differential equations (eg Chapter 2 of Evans’ Partial Differential Equations).
  • Helpful:
    • Differential geometry of curves and surfaces.

Pre-Reading

  • L.C. Evans, Partial Differential Equations (Chapter 2)
Associate Professor Julie Clutterbuck

A. Prof. Julie Clutterbuck
Monash University, Australia

Julie grew up in country Victoria, east of Melbourne. She completed at PhD at the Australian University with Ben Andrews, then held positions at ANU and Freie Universität Berlin before taking up a lectureship at Monash. Julie’s research is in geometric analysis, looking at partial differential equations of particular importance in geometry. She has a small black dog, and this year started playing trombone in a band.