A/Prof. Brailey Sims

Qualifications

• PhD, University of Newcastle
• Bachelor of Science (Honours), University of Newcastle
• Bachelor of Science, University of Newcastle

Research

Research keywords

• Banach space geometry
• Functional Analysis
• Metric fixed point theory
• Nonlinear Analysis
• Ultraproducts of metric and Banach space

Research expertise

Sims' broad area of research is functional and nonlinear analysis, in which he has published over 60 refereed research papers in major international journals. More specifically his interest and expertise is in geometry in both Banach spaces and convex metric spaces, attainment problems and the use of embedding techniques (for example, embedding into ultrapowers) for solving such problems. His investigations have included attainment problems associated with boundary points of operator numerical ranges, and more recently the attainment of fixed points by various classes of mappings.

Nonlinear optimization and control leads to variational inequalities and hence to fixed points. Equilibria of dynamical systems correspond to fixed points, whose approximability relate to the stability and ergodic behaviour of the system. The research aims to further our understanding of nonexpansive type mappings, with an emphasis on establishing easily verified, yet widely applicable, criteria for the existence of a fixed together with effective iterative algorithms for their approximation. Of particular interest are the little understood cases where the underlying space admits no natural linear structure or nice geometry, so the usual tools of convex analysis are inapplicable. Geodesic metric spaces and notions of hyperbolicity are a fertile setting for investigations while ultraproduct methods provide powerful techniques.

Fields of Research

Centres and Groups

Centre

• PRC - Centre for Complex and Dynamic Systems and Control
• PRC - Computer Assisted Research Mathematics and its Applications
• PRC - Computer Assisted Research Mathematics and its Applications

Memberships

Committee/Associations (relevant to research).

• Fellow - Australian mathematicval society

Editorial Board.

• Assistant Editor - Journal of Mathematical Analysis and Applications
• Associate Editor - Jourenal of Nonlinear Analysis - Theory, Methods and Applications
• Assistant Editor - Journal of Fixed Point Theory and Applications

Invitations

Administrative

Administrative expertise

Head of Department/School

Deputy President of Academic Senate

Member of numerous selection and diverse other University Committies.

Teaching

Teaching keywords

• All areas at undergraduate level
• At all levels
• Functional analysis at graduate level

Teaching expertise

Sims has taught undergraduate courses in most areas of pure mathematics, and some in applied mathematics; in particular mathematical modelling in the life sciences, operations research and optimization. These have been at all levels; pre-undergraduate to honours and to students of all ability levels.