Analysis & Topology

Members of the Analysis and Topology cluster in the De Brún Centre undertake research in: 

• Fractal Geometry: Attractors and Semiattractors of Iterated Function Systems; Invariant Measures (Nina Snigireva)

• Functional analysis: Polynomials and Holomorphic Functions on Banach Lattices (Nina Snigireva)
  
  
• Topological graph theory (James Cruickshank)
  
• Nonlinear analysis (Donal O’Regan) 
  
  
• Numerical analysis of PDEs (Niall Madden) 
  
  
• Computational Topology (James Cruickshank, Graham Ellis)

Research in topological graph theory in the cluster focuses on embedded graphs that arise naturally from problems in discrete geometry and in graph drawing.

Research in numerical analysis focuses on the mathematical foundations of algorithms for solving partial differential equations whose solutions feature boundary and/or interior layers. Recent work includes the analysis of weighted finite element methods, algorithms for adaptive mesh generation, and fast solvers for finite difference and finite element discretizations. 

Cluster members: James Cruickshank, Niall Madden, Aisling McCluskey, Donal O'Regan, Nina Snigireva 

Emeritus Cluster members: John Burns,  Graham Ellis, Ray Ryan, Jerome Sheahan