Pure Mathematics Research Areas

Professor Martin Bunder

Illative combinatory logic and lambda calculus as a foundation of logic and mathematics.
Systems of type theory including simple types, intersection types and pure type systems. Also the relations between these and illative combinatory logic.
Nonclassical logics and proof generating algorithms for these.
BCK and BCI algebras and their relations with logics.
Elementary Number Theory - in particular properties of certain integer sequences.

Dr James McCoy

James McCoy is a 'geometric analyst' whose main research interests are questions related to second- and higher order-nonlinear curvature flows of hypersurfaces. Such questions include long time existence of globally constrained curvature flows, formation of singularities (where the curvature becomes unbounded) in curvature flows and extension of classical flow solutions beyond singularities using a 'surgery' procedure. Such analysis relies heavily on techniques from differential geometry, elliptic and parabolic partial differential equations, functional analysis and topology.

James is also interested in modelling proteins and related structures using the calculus of variations.

Associate Professor Peter Nickolas

Topological groups: subgroups of free topological groups and free products of topological groups, and certain general properties of topological groups, usually outside the realm of locally compact groups.
Geometry of metric spaces.

Professor Rod Nillsen

Harmonic analysis, emphasising finite differences, the Fourier transform and multiplier theory
Chaos, randomness and ergodic theory

Associate Professsor David Pask

Functional Analysis, Operator Algebra, Nonabelian Duality

Professor Jacqui Ramagge

Topological groups, including Kac-Moody groups.
Applications of geometric group theory to harmonic and functional analysis.
Hecke algebras, including their C*-completions.

Dr Aidan Sims

Broadly in the area of functional analysis and abstract harmonic analysis. Particularly the area of research is operator algebras. Specifically Cuntz-Krieger algebras of directed graphs and their analogues, as well as product systems and associated operator algebras. Aidan has more recently developed interests in representation theory for groupoids, and in Dixmier-Douady theory.

Dr Caz Sandison

Topological group theory. In particular the variety of topological groups
generated by the class of all Banach spaces, the variety generated by the
class of all locally compact abelian groups and the variety generated by
the free abelian topological group on [0,1].