New Zealand Institute of Mathematics & its Applications (NZIMA)

Programme theme: The programme centres around the design and analysis of algorithms, and their application to contemporary problems in such areas as discrete mathematics, computational biology, social sciences, and communication networks. Particular emphasis will be placed on the following areas and the interaction between them: randomized algorithms; probabilistic analysis of algorithms; approximation algorithms; fixed-parameter tractability.

Conformal Geometry and its Applications

Programme theme: (i) Conformal and hyperbolic geometry: conformally compact structures, hyperbolic and, more generally, asymptotically hyperbolic Poincare-Einstein metrics; conformally flat manifolds via differential geometry and via Kleinian groups - exploring links; geometric analysis.
(ii) Symmetries and natural geometric equations: approaches to overdetermined PDE and elliptic operators by prolonged systems and symmetries; geometric structure of DEs and PDEs - links to conformal and related geometries; applications in hyperbolic geometry, Riemannian geometry and conformal geometry; applications in other areas - including discretisation for numerical calculations and applications in physics
(iii) Invariants and applications: general theory of invariants of geometric structures - especially conformal and hyperbolic structures and links to topological data; scattering and asymptotic invariants of conformally compact structures; invariants of DE and PDE - invariants giving coordinate independent characterisations of DE/PDE, invariants obstructing solutions.
(iv) Nonlinear elasticity and materials science: the governing equations of nonlinear elasticity and (theoretical) materials science and those of conformal geometry are basically the same. Key problems in materials science are bridging length structures and analysing fractal microstructures. Conformal geometry would seem to supply the tools for this. We intend to explore connections between our knowledge of these fields and those of more applied researchers in these areas.