A circle packing used to compute an intrinsic circle domain Heilbronn Institute for Mathematical Research Edward Crane

Edward Crane

Senior Heilbronn Research Fellow, University of Bristol

Research topics Probability, Circle packings, Geometric Function Theory.
Email edward dot crane at bristol dot ac dot uk
Postal address Department of Mathematics, Howard House,
  Queens' Avenue, Bristol BS8 1SN, United Kingdom.


Age evolution in the mean field forest fire model via multiype branching processes. With Balazs Rath and Dominic Yeo.

Steady state clusters and the Rath-Toth mean field forest fire model.

Diffusion and superdiffusion in lattice models of colliding particles with stored momentum. With Sean Ledger and Balint Toth.

Functional large deviations for Cox processes and Cox/G/∞ queues, with a biological application. With Justin Dean and Ayalvadi Ganesh.

Slides from recent talks

A talk for 6th form maths students about sums of two squares: "Pythagoras hits the prime time!"

A short talk on the mean field forest fire model (13th Jan 2014)

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

Conferences that I've helped to organise:

PAD21@Bristol: Probability, Analysis and Dynamics at Bristol, April 7-9 2021.

PAD18@Bristol: Probability, Analysis and Dynamics at Bristol, April 4-6 2018.

PAD@Bristol: Probability, Analysis and Dynamics at Bristol, April 23-25 2014.

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 6 (2006) no. 1, 145--164.

Mean value conjectures for rational maps (2006)
Complex Variables and Elliptic Equations, 51, no. 1 (January 2006), 41-50.

On Keogh's length estimate for bounded starlike functions (2005)
With Dinesh Markose
Computational Methods and Function Theory
, 5, (2005) no. 2, 263--274.

The area of polynomial images and pre-images (2004)
Bulletin of the London Mathematical Society 36, no. 6 (November 2004), 786-792.


PhD Thesis

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.