Research

I’m mainly interested in geometry and topology (with differential flavour).

Undergraduate Projects

• Einstein Manifolds

  4th year dissertation; Supervised by Jason D. Lotay

• The Isoperimetric Inequality (& Curve Shortening Flow)

  3rd year extended essay; Supervised by Jason D. Lotay
  [report] We discuss some results in the study of the isoperimetric inequality and curve shortening flow that share a similar theme. We discuss the relationship between the isoperimetric inequality, Wirtinger’s inequality and Sobolev inequality. We also discuss the support function method and the level set method of attacking curve shortening flow.

• Applications of Lie Groups to Differential Equations

  2nd year summer project; Supervised by Jason D. Lotay
  [report] The symmetry group of a differential equation is the largest group of transformations acting on independent and dependent variables with the property that it transforms solutions to other solutions. The symmetry group often gives us greater insight into the differential equation. We would demonstrate the symmetry groups of the heat and wave equation.