## 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.