My research interests lie in dynamical systems and ergodic theory. In particular, hyperbolic dynamical systems, which display rich orbit structures and exhibit chaotic properties. It is fruitful to take a statistical viewpoint when confronted with a complicated orbit structure: rather than trying to understand every orbit, we instead consider typical orbit behaviour. In this way ergodic theory studies phenomena related to dynamical systems and, more generally, group actions. Examples of these phenomena include statistical asymptotics, periodic point structure and classifying invariant measures.
My current research investigates asymptotics associated to free groups. Of particular interest are the asymptotics that arise from restricting the group elements to a non-trivial conjugacy class. We draw upon techniques from the thermodynamic formalism, the transfer operator method and symbolic dynamics for hyperbolic groups.
I am a fourth year PhD student (expected completion summer 2017) under the supervision of Professor Richard Sharp.
I chair the department's Staff and Graduate Student Liaison Committee (SGSLC). The committee meets once per term to discuss postgraduates' academic and pastoral welfare. As SGSLC chair, I represent the maths PG community at departmental Teaching Committee and Staff meetings, volunteer at the PG induction and organise the PG Christmas Party.
I have TA'd for the following mathematics courses: Analysis I, Analysis II, Dynamical Systems, Experimental Maths and Metric Spaces. I regularly assist at Warwick's Further Maths Support Programme outreach events including: STEP study sessions, student enrichment days, Royal Institution workshops and problem solving conferences. In 2015 I won a departmental award for inspirational teaching.
Kenison, G. and Sharp, R. Orbit counting in conjugacy classes for free groups acting on trees, to appear in the Journal of Topology and Analysis (pdf).