PhD thesis

Supervised by Marcy Robertson at the University of Melbourne

My aim is to construct a particular example of a cyclic infinity operad based on surfaces, known as the surface operad.  This work is in algebraic topology, the following areas in particular:

  • Infinity operads and dendroidal sets
  • Cyclic operads, modular operads, and other extensions to operads
  • Cobordisms and Topological Quantum Field Theories
  • Asteroidal sets (a model for infinity cyclic operads based on the simplicial and dendroidal models)

Honours thesis

Supervised by Dan Mathews at Monash University

Inspired by Contact Geometry and Topological Quantum Field Theories, there
is the notion of a Contact Representable Finite State Automaton (FSA). This
project explored the relationships between Contact Geometry, TQFTs, FSAs
and Semigroups. In particular, I was able to show that groups are unable to be represented by certain types of contact structures.