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

Edward Crane


Senior Heilbronn Research Fellow, University of Bristol

Research topics Geometric function theory, circle packings, and probability.
Email edward dot crane at bristol dot ac dot uk
Postal address Department of Mathematics, Howard House,
  Queens' Avenue, Bristol BS8 1SN, United Kingdom.

Slides from recent talks

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

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

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


Publications

Intrinsic Circle Domains.
To appear in Conformal Geometry and Dynamics

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.
Ann. Probab. 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.


 

Teaching

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.