Analysis & Topology

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

• Attractors and Semiattractors of Iterated Function Systems; Invariant Measures; Polynomials and Holomorphic Functions on Banach Lattices (Nina Snigireva) 

• Fractal geometry and geometric measure theory. 

• Functional analysis. 

• Geometric rigidity theory (James Cruickshank). 

• Nonlinear analysis (Donal O’Regan) 

• Numerical analysis of PDEs (Niall Madden) 

Geometric Rigidity Theory studies bar and joint frameworks and various other related structures. Recent work is on rigidity theory of surface graphs and other related families of graphs such as block and hole graphs. This involves ideas from algebraic geometry, graph theory and low-dimensional topology. 

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