Research topics | Probability, Circle packings, Geometric Function Theory. |

edward dot crane at bristol dot ac dot uk | |

Postal address | Department of Mathematics, Howard House, |

Queens' Avenue, Bristol BS8 1SN, United Kingdom. |

A talk for prospective PhD students given at the LMS Prospects in Mathematics 2013 conference at the University of Durham.

Workshop on Hyperbolic Geometry in Complex Analysis 3rd-7th September 2007

Circle Packings with Generalized Branching. With James Ashe and Ken Stephenson.

To appear in Journal of Analysis, special volume for the retirement conference of David Minda.

Cluster growth in the dynamical Erdos-Renyi process with forest fires

With Nic Freeman and Balint Toth. Electronic Journal of Probability 20 (2015) no 101, 33 pages.

Intrinsic Circle Domains.

Conformal Geometry and Dynamics 18 (2014), 65-84

Relative Riemann mapping criteria and hyperbolic convexity (2012)

Proc. Amer. Math. Soc. 140 (2012) no. 7, 2375-2382.

The simple harmonic urn (2010)

With Nicholas Georgiou, Stanislav Volkov,
Andrew Wade and Robert Waters.

Annals of Probability 39 (2011), no. 6, 2119-2177.

Rigidity
of configurations of balls and points in the N-sphere (2010)

With Ian Short.

Q. J. Math. 62 (2011), no. 2, 351-362.

A note on the Hayman-Wu theorem (2008)

*Computational Methods and Function Theory* vol. 8, issue 1-2, pp. 615-624

Conical limit sets and continued fractions (2007)

With Ian Short.

*Conformal Geometry and Dynamics*, 11 (2007), 224-249.

A bound for Smale's mean value conjecture for complex polynomials (2007)

*Bulletin of the London Mathematical Society*, vol. 39, No. 5, 781--791.

Extremal polynomials in Smale's mean value conjecture (2006)

* Computational Methods and Function Theory*

Mean value conjectures for rational maps (2006)

* Complex Variables and Elliptic Equations*,

On Keogh's length estimate for bounded starlike functions (2005)

With Dinesh
Markose *
Computational Methods and Function Theory*,

The area of polynomial images and pre-images (2004)

*Bulletin of the London Mathematical Society*

You may be interested in parts of my PhD thesis, entitled "Topics in Conformal Geometry and Dynamics". If you want to print specific pages, it may help you to know that there are fourteen pages before chapter 1 begins on page 1.

Undergraduate course: Combinatorial Enumeration, part of a shared course, "Topics in Discrete Mathematics" at the University of Bristol (2013).

Graduate course: Dynamics of Rational Functions University of Bristol, (2007)

© University of Bristol, 2007-2013. Last updated: 13/01/2014.