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.

Dr James McCoy

James McCoy is a 'geometric analyst' whose main research interests are questions related to nonlinear curvature driven heat-type 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.

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.
• Applications of logic to software verification, and protocol verification.

Associate Professor Rod Nillsen

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

Associate Professsor David Pask 

Functional Analysis, Operator Algebra, Nonabelian Duality

Dr Frank Prokop

• Topology: Generalisations of topologies and continuous functions
  to partially ordered sets and lattices.
  
• Partially ordered sets: neighbourhood and bi-neighbourhood
  structures and generalised continuity extended to partially ordered sets.
  
• Neighbourhood lattices: generalised continuity and convergence in.

Professor Iain Raeburn 

Operator algebras

Associate Professor Jacqui Ramagge 

• Topological groups, including Kac-Moody groups. 
•  Harmonic and functional analysis, particularly harmonic analysis of groups acting on buildings. 
•  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.

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].

Associate Professor Graham Williams

• Partial differential equations
• Control theory for distributed systems
• Calculus of variations
• Differences spaces