Andrew Francis Research 
Other Sites
Contact details
Professor Andrew R. Francis

Director, Centre for Research in Mathematics,
School of Computing, Engineering and Mathematics
, Western Sydney University
Room 1.42, Building EN, Parramatta Campus.

  • Potential PhD students or honours students in algebraic biology - please contact me to discuss enrolment and scholarship options. 
  • Interested in doing research at Western Sydney?  We welcome discussions about applications for ARC DECRA or Future Fellowships.

Research.  Publications

While my research training is in pure mathematics, I currently research in several areas, principally in algebra and in mathematical biology.  Lately I have been developing the applications of algebraic ideas to bacterial evolution, and have written an expository paper available from J. Math. Biol. (or on the arxiv). More papers on this theme can be found in my list of publications, here.

algebra research has focussed on questions about the structure of Iwahori-Hecke algebras of finite reflection groups (Coxeter groups in the real case). Most questions I have looked at relate to the structure of the centres of these algebras (that part which commutes with all other elements in the algebra). These topics lie within the representation theory of finite groups. Finite groups are ubiquitous in many parts of mathematics and sciences more broadly, and questions about their structure can often be accessed by considering how they can be "represented" within groups of matrices. This question in turn led historically to the study of Iwahori-Hecke algebras, which are deformations, or "q-analogues", of the group algebras of finite reflection groups. 

My mathematical biology work began with the question of how to best understand the immensely detailed genetic data arising from an outbreak of infectious disease such as tuberculosis. More recently I have been working on understanding the evolutionary processes behind the structure of bacterial genomes.  In general, I am interested in how mathematics can help describe the processes underlying the science we observe. This work has been with a number of collaborators (notably A/Prof Mark Tanaka at UNSW), and has been funded by several ARC Discovery Grants (2005-2007, 2009-2013, 2013-2015), and by an ARC Future Fellowship (2010-2014) that focusses on the use of algebra to study evolution.  

Our 2009 paper, "The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis" by Fabio Luciani, Scott Sisson, Honglin Jiang, Andrew Francis and Mark Tanaka in Proceedings of the National Academy of Sciences of the USA (August 2009), has received media attention, e.g.: an interview on ABC Radio National PM, an article on ABC Science Online, an article in the Sydney Morning Herald

I have several other active research programmes that relate to the above, including some recent work on phylogenetic networks with Mike Steel (Canterbury), and work on algebraic statistics with Henry Wynn (LSE).

Research students.  I am interested in recruiting suitably qualified honours or PhD students in both algebra and mathematical biology, please contact me if interested.

Current research students: Sangeeta Bhatia, Stuart Serdoz, Tanzila Chowdhury, Chad Clark, Michael Hendriksen.

Recent students include Brent Le Cornu (honours 2009), who completed a project on knot invariants and has now just finished a PhD in plasma physics at UWS, Tanzila Chowdhury (2015) who worked drug resistance in tuberculosis, and Stuart Serdoz (2012), Terry Bowers (2011) and Chad Clark (2015), who all worked on modelling bacterial evolution using group theory.  I regularly supervise undergraduate research projects. Recent topics include Symmetric polynomials, the Geometry of reflection groups, Galois theory, Cyclotomic polynomials, The Robinson-Schensted correspondence, and Bacterial genome organization.

Other sites of interest.

Haldane's Sieve. A site that enables discussion of recent preprints in population and evolutionary genetics.
The Genealogical World of Phylogenetic Networks. Biology, anthropology, computational science, and networks in phylogenetic analysis. A blog managed by several people with interesting ideas and comments on phylogenetic networks.
TED: Ideas worth spreading. This site contains video talks on a wide range of topics by leading thinkers from around the world.  Worth a look!

12 Canoes. This is an astonishingly beautiful series of short films by and about the Yolngu people of Central Arnhem Land in the Northern Territory of Australia, in collaboration with the director of the film 10 Canoes.

Contact details:

Prof. Andrew Francis, 
Centre for Research in Mathematics,
School of Computing, Engineering and Mathematics,
Western Sydney University (Parramatta campus),
Locked Bag 1797,
Penrith, NSW 2751,

Phone: +61-2-9685 9236 
Fax: +61-2-9685 9245 
Email: a.francis (at) westernsydney (dot) edu (dot) au