Jonathan Reynolds

From July 2009-2011 I'm a Marie Curie Intra-European Fellow at Utrecht University. My main research area is Number Theory. In particular, I study interactions between the arithmetic of divisibility sequences and the solvability of Diophantine equations. Also, I'm starting to study the connections with Dynamical Systems.

Curriculum Vitae

An Open Question
Suppose that x^3-y^2=2z^6, where x,y,z are nonzero pairwise coprime integers. If z is a perfect power then does z=1?
 

Email: jonathan.reynolds@gmx.com

Skype: jonathan.reynolds7

WHERE I AM

From 21 Apr 2012 - 16th May 2012 I will be at the Universidad de Concepción .
From 26th Nov - 3rd Dec 2011 I visited the University of Crete.
From 9th-23rd Apr 2011 I visited the University of British Columbia.

TEACHING: RATIONAL POINTS ON ELLIPTIC CURVES

PREPRINTS

Q-curves and elliptic divisibility sequences, with Sander Dahmen.

PUBLISHED

Matrix divisibility sequences, with Gunther Cornelissen, Acta Arithmetica (accepted).
Perfect powers in elliptic divisibility sequences, J. Number Theory 132 998-1015 (2012).
Perfect powers generated by the twisted Fermat cubic, Funct. Approx. Comment. Math. 46(1) 133-145 (2012).
On the pre-image of a point under an isogeny and Siegel's theorem, New York J. Math. 17 163-172 (2011).
On the denominators of rational points on elliptic curves, with G. Everest and S. Stevens, Bull. London Math. Soc. 39(5) 762-770 (2007).

PHD THESIS

Extending Siegel's Theorem for Elliptic Curves. On 19th March 2008 I was examined by Prof. John Cremona and Prof. Thomas Ward. My supervisors were Prof. Graham Everest and Prof. Shaun Stevens. Some theorems in this thesis can be developed further and some questions which arise have now been resolved, full details are given here (coming soon).

TALKS

Divisibility sequences and Diophantine equations at the University of Crete in Decemeber 2011.
Perfect powers generated by the twisted Fermat cubic at the Utrecht Number Theory Seminar in March 2011.
Modular methods for perfect powers in elliptic divisibility sequences at the Intercity Number Theory Seminar in February 2011.
Power integral points on elliptic curves at the Intercity Number Theory Seminar on 4th December 2009.
Power integral points on elliptic curves at Warwick Number Theory Seminar on 7th April 2008 and UEA Pure Seminar on 28th April 2008.
A generalization of Siegel's theorem and Level lowering at UEA Arithmetic Seminar on 13 November 2006 and 13 December 2007 respectively.