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Dr Steve Baigent
  • Reader in Mathematics
  • Dept of Mathematics
  • Faculty of Maths & Physical Sciences
Oxford University 1981-1987, BA, MSc DPhil Mathematics.

Research Summary

My research focus is dynamical systems, especially those derived from models from ecology. In particular, I am concerned with the existence of invariant manifolds, their geometry, and how this geometry can be used to study the long-term dynamics of the system. Much of my work involves systems that enjoy an ordering property, such as monotone or competitive systems. Originally I worked with continuous time models, but increasingly I have treated models with discrete time. In my work some form of balance is in operation. For example, in ecology growth balances decline along a manifold known as the carrying simplex. In genetics, there is a balance between recombination and selection along a manifold which is close to the well-known Hardy-Weinberg manifold. The identification of processes that balance in models is an important step towards simplifying the model and analysing its behaviour.

Teaching Summary

MATH3506/MATHG506 Mathematical Ecology. 

 30 lectures covering the basic models that describe the evolution of populations, and those from which operational models in, say, fisheries or disease spread are built. The course covers singles species models in continuous and discrete time, 2 species models in continuous time via phase plane analysis, Leslie matrix age-structured models and finally general Lotka-Volterra systems.

MATHM505/MATHG505 Evolutionary Game Theory and Population Genetics

30 lectures split into two equal parts. The first part is an introduction to evolutionary game theory including the concepts of Nash equilibria and Evolutonarily Stable States/Strategies. An analysis of replicator systems and Bimatrix games. In the second part, the Wright-Fisher model, and models for selection, recombination and mutation are studied.

Academic Background
1995 DPhil Doctor of Philosophy – Mathematical Modelling University of Oxford
1987 MSc Master of Science – Mathematical Modelling University of Oxford
1985 BA Bachelor of Arts – Mathematics University of Oxford
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