PhD thesis

Supervised by Marcy Robertson at the University of Melbourne

My work has revolved around topological examples of higher operads, in particular constructing a cyclic infinity operad of surfaces.  I have explored topics such as:

  • 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.