Professor Chris Good BA, MA (Oxon), DPhil (Oxon)

Dr Chris Good

School of Mathematics
Professor of Mathematics
Deputy Head of School

Contact details

Address
School of Mathematics
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Chris Good is Professor of Mathematics at the University of Birmingham. He is the author of over 50 research articles in general topology, set-theoretic topology, topological dynamics and mathematical education.  He regularly collaborates with mathematicians around the world, including colleagues from Mexico, New Zealand, Poland and the US, as well as from Oxford, and has organised conferences in Birmingham, Oxford and Cambridge.  Chris has worked with several postdoctoral fellows and supervised a number of graduate students.  If you are interested in working with him, he would be interested in hearing from you.

Chris has a long standing interest in teaching and was awarded the first Head of School’s Excellence in Teaching Award.  He played a leading role in the development of the School’s new curriculum, championing the introduction of problem based learning and core skills.


For more information, visit Chris’s School web page: web.mat.bham.ac.uk/C.Good/

School web page: web.mat.bham.ac.uk/C.Good/

Qualifications

  • DPhil in Mathematics (Oxon) 1992
  • MA (Oxon) 1991
  • BA in Mathematics (Oxon) 1988

Biography

Chris studied Mathematics at the Queen’s College, University of Oxford, graduating with first class honours in 1988. He completed his DPhil whilst a Junior Research Fellow at Wadham College before joining the School of Mathematics at the University of Birmingham in 1995. He was promoted to Senior Lecturer in 2001, Reader in 2012, and Professor in 2016.

Chris’s early research was in the construction of counterexamples (often using set-theoretic methods) especially around the Dowker space question and the behaviour of normality in product spaces.  He also looked at the role of the Axiom of Choice in topology and has worked extensively on generalised metric spaces, in particular g-functions and monotonicity.  More recently he has become interested in dynamical systems, in particular symbolic dynamics and the structure of invariant sets, and abstract topological dynamics.  When he is not doing mathematics, Chris loves to cook, play rugby, read, listen to music and spend time running around with his young family. He is interested in politics and the natural world.

Teaching

Chris has taught over 18 different modules at all levels, ranging from Foundation Year Mathematics, through First Year Probability and Statistics, to advanced topics in pure mathematics such as General Topology, Complex Analysis and Discrete Dynamics.  He has supervised many undergraduate projects as well as undergraduate Summer research projects.  He introduced the First Year enquiry based learning modules ‘Developing Mathematical Reasoning’ (based on the influential Moore Method, with the aid of a grant from the Educational Advancement Foundation) and ‘Mathematical Modelling and Problem Solving’ and the Second Year problem solving and skills module ‘Mathematics in Industry’ (with the aid of a grant from the HE STEM Programme).

Postgraduate supervision

Chris is keen to supervise students in either set-theoretic and general topology or discrete dynamical systems and topological dynamics.  For more information about his current and past graduate students and their work please see Chris’s web page web.mat.bham.ac.uk/C.Good/

  • Lylah Haynes, PhD (2006): Monotonizations of countable paracompactness.
  • Tom Parker, MPhil (2007): Sharkovskii's theorem and chaotic dynamical systems.
  • Andrew Barwell, PhD (2011): ω-limit sets of discrete dynamical systems.
  • Syahida binti Che Dzul-Kifli is currently looking at definitions of chaos.
  • Amna Ahmed is currently looking at the structure of continuous and order preserving maps on the rational numbers.
  • Kyriakos Papadopoulos is currently looking at characterizations of ordinals.

PhD opportunities

Research

RESEARCH THEMES

  • Topological dynamics: Even simple looking functions, such as the logistic or quadratic map, when iterated can exhibit complex and chaotic behaviour. This behaviour can be studied from a topological point of view.
  • Abstract dynamics: Let T be a function from the set X to itself. Abstract dynamics asks under what conditions a structure can be imposed on X with respect to which T has some meaning. For example, one might ask whether a particular abstract system T:X→X can be modelled as a continuous self-map of a compact Hausdorff space, so that there is a compact Hausdorff topology on X with respect to which T is continuous.
  • The term generalized metric is a catch all for topological spaces that share some of the structures of metric spaces. The interrelationships between these structures form a rich and varied theory.

RESEARCH ACTIVITY
Recently Chris has been working on:

  • The structure of ω-limit sets of tent maps and shifts of finite type using a mixture of analytic and symbolic techniques.
  • Countable dynamical systems.
  • The dynamics of included maps on hyperspaces.
  • Abstract dynamical systems modelled by compact Hausdorff spaces, separable metric spaces, the space of rational numbers and continua.
  • Coarse graining and dimensioonal reduction of dynamical systems .

Other activities

Chris is Deputy Head of School.

Publications

For a complete list of Chris’s publications and links to copies of his papers please go to web.mat.bham.ac.uk/C.Good/research/pubs-cites.pdf

Good, C., (1995), Large cardinals and small Dowker spaces, Proceedings of the American Mathematical Society, 123: 1, 263--272

Good, C. and Tree, I. J., (1995), Continuing horrors of topology without choice, Topology and its Applications, 63: 79--90 

Good, C., Knight R. W. and Stares I. S., (2000), Monotone countable paracompactness, Topology Appl., 101: 281--298 

Good, C., Knight R. W., (2006), Monotonically countably paracompact, collectionwise Hausdorff spaces and measurable cardinals, Proc. A.M.S., 134: 591--597 

Good, C., Greenwood, S. R., Knight, R. W., MacIntyre, D. W., and Watson, W. S., (2006), Characterizing continuous functions on compact, Hausdorff spaces, Advances in Mathematics, 206: 695--728. 

Good C., Knight, R. W. And Raines, B. E., (2006), Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities, Fundamenta Mathematicae, 192: 267--289 

Good, C. and Haynes, L., (2007), Monotone versions of countable paracompactness , Topology Appl., 154: 734--740 

Good, C., Kight, R. W. and Raines, B. E., (eds), (2009), Topology Appl. (Special Issue): A conference in honour of Peter Collins and Mike Reed, 156 

Good, C. and Greenwood, S. R., (2010) Continuity in separable metrizable and Lindel\"of spaces, Proc. A.M.S., 138: 577--591 

Barwell, A., D., Good, C., Knight, R. W. and Raines, B., E., (2010) A characterization of $\w$-limit sets of shifts of finite type and tent maps, Ergodic Theory and Dynamical. Systems, 30: 21--31

Media experience

Expertise: Mathematics

Experience:  Chris has worked on a number of videos for the School.  He has given public talks and has appeared in videos on YouTube for Meet the Mathematicians.