## Professional biography

Dr Ian Short is the Director of Research in Mathematics and Statistics and a Senior Lecturer in Analysis. He joined the Open University in 2010 having previously worked as a researcher and developer at the University of Cambridge and the National University of Ireland, Maynooth. Ian has a BSc, an MSc, and a PhD, all in mathematics from the University of Cambridge.

## Research interests

Ian's research interests in mathematics include topics in complex analysis, continued fraction theory, dynamical systems, and hyperbolic geometry.

Recent research interests include:

*Classifying SL2-tilings*https://arxiv.org/abs/1904.11900. This work describes a new, unifying approach to classifying SL2-tilings using the geometric, numeric, and combinatorial properties of the Farey graph.*Dynamics of hyperbolic isometries*https://arxiv.org/abs/1609.00576. This paper is about how dynamical systems involving hyperbolic isometries can be interpreted using the theory of semidiscrete semigroups of hyperbolic isometries, which is developed from first principles.*Necessary and sufficient conditions for convergence of continued fractions*. This research is about an attractive, simple algorithm for determining whether an integer continued fraction converges.

## Teaching interests

Ian is chair of the undergraduate module M337 *Complex analysis* and the MSc module M829 *Analytic number theory II*.

He chaired the rewrite of M337, completed in 2018. The revised books for M337 have approximately 1150 pages, well over 1000 figures, and a wealth of exercises and solutions. Here are the four beautifully illustrated module texts and the module handbook:

Before writing M337, Ian was an author of the modules MST124 *Essential mathematics 1* and MST125 *Essential mathematics 2*.

## Publications

### Journal articles

**Repeated compositions of Möbius transformations (2020)**

Jacques, Matthew and Short, Ian

Ergodic Theory and Dynamical Systems, 40(2) (pp. 437-452)

**Normal families of Möbius maps (2020)**

Beardon, Alan; Minda, David and Short, Ian

Computational Methods and Function Theory ((In press))

**Escaping sets of continuous functions (2019-03)**

Short, Ian and Sixsmith, David J.

Journal d'Analyse Mathematique, 137(2) (pp. 875-869)

**A hyperbolic-distance inequality for holomorphic maps (2019)**

Short, Ian and Christodoulou, Argyrios

Annales Academiæ Scientiarum Fennicæ, Mathematica, 44 (pp. 293-300)

**Substitution-based structures with absolutely continuous spectrum (2018-08-31)**

Chan, Lax; Grimm, Uwe and Short, Ian

Indagationes Mathematicae, 29(4) (pp. 1072-1086)

**Geodesic Rosen Continued Fractions (2016-12-30)**

Short, Ian and Walker, Mairi

The Quarterly Journal of Mathematics, 67(4) (pp. 519-549)

**The parabola theorem on continued fractions (2016-04-11)**

Short, Ian

Computational Methods and Function Theory, 16(4) (pp. 653-675)

**A geometric representation of continued fractions (2014-05)**

Beardon, Alan F. and Short, Ian

American Mathematical Monthly, 121(5) (pp. 391-402)

**Maximal buttonings of trees (2014)**

Short, Ian

Discussiones Mathematicae Graph Theory, 34(2) (pp. 415-420)

**On the product decomposition conjecture for finite simple groups (2013-11)**

Gill, Nick; Pyber, László; Short, Ian and Szabó, Endre

Groups, Geometry, and Dynamics, 7(4) (pp. 867-882)

**Conformal automorphisms of countably connected regions (2013-01-09)**

Short, Ian

Conformal Geometry and Dynamics, 17 (pp. 1-5)

**Conjugacy in Thompson's group $F$ (2013)**

Short, Ian and Gill, Nick

Proceedings of the American Mathematical Society, 141 (pp. 1529-1538)

**Hausdorff dimension of sets of divergence arising from continued fractions (2012-04)**

Short, Ian

Proceedings of the American Mathematical Society, 140(4) (pp. 1371-1385)

**Flowability of plane homeomorphisms (2012)**

O'Farrell, Anthony; Le Roux, Frédéric; Roginskaya, Maria and Short, Ian

Annales de l'Institut Fourier, 62(2) (pp. 619-639)

**Geodesic continued fractions (2012)**

Beardon, A. F.; Hockman, M. and Short, I.

Michigan Mathematical Journal, 61(1) (pp. 133-150)

**Visualizing uncertainty about the future (2011-09-09)**

Spiegelhalter, David; Pearson, Mike and Short, Ian

Science, 333(6048) (pp. 1393-1400)

**Rigidity of configurations of balls and points in the**

*N*-sphere (2011-06-29)Crane, Edward and Short, Ian

The Quarterly Journal of Mathematics, 62(2) (pp. 351-362)

**Ford circles, continued fractions, and rational approximation (2011-02)**

Short, Ian

American Mathematical Monthly, 118(2) (pp. 130-135)

**The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions (2010-06)**

Beardon, Alan F. and Short, Ian

Bulletin of the London Mathematical Society, 42(3) (pp. 457-466)

**Norms of Möbius maps (2010-06)**

Beardon, Alan F. and Short, Ian

Bulletin of the London Mathematical Society, 422(3) (pp. 499-505)

**Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line (2010-03)**

Gill, Nick and Short, Ian

Aequationes Mathematicae, 79(1-2) (pp. 23-37)

**Reversibility in the group of homeomorphisms of the circle (2009-10)**

Gill, Nick; O'Farrell, Anthony G. and Short, Ian

Bulletin of the London Mathematical Society, 41(5) (pp. 885-897)

**Conjugacy classification of quaternionic Möbius transformations (2009)**

Parker, John R. and Short, Ian

Computational Methods and Function Theory, 9(1) (pp. 13-25)

**Reversibility in the diffeomorphism group of the real line (2009)**

O'Farrell, Anthony and Short, Ian

Publicacions Matemàtiques, 53(2) (pp. 401-405)

**Reversible maps in isometry groups of spherical, Euclidean and hyperbolic space (2008-09-18)**

Short, Ian

Mathematical Proceedings of the Royal Irish Academy, 108A(1) (pp. 33-46)

**How much money do you need? (2008-01)**

Short, Ian

Mathematical Spectrum, 40(2) (pp. 67-72)

**Conical limit sets and continued fractions (2007-10-31)**

Crane, Edward and Short, Ian

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

**Conformal symmetries of regions (2007-07)**

Beardon, Alan F. and Short, Ian

Irish Mathematical Society Bulletin, 59(1) (pp. 49-60)

**Reversible maps in the group of quaternionic Möbius transformations (2007)**

Lávička, Roman; O'Farrell, Anthony G. and Short, Ian

Mathematical Proceedings of the Cambridge Philosophical Society, 143(1) (pp. 57-69)

**Van Vleck's theorem on continued fractions (2007)**

Beardon, Alan F. and Short, Ian

Computational Methods and Function Theory, 7(1) (pp. 185-203)

**Magic letter groups (2007)**

Short, Ian and Pearson, Mike

Mathematical Gazette, 91(522) (pp. 493-499)

**Hyperbolic geometry and the Hillam-Thron theorem (2006-04-07)**

Short, Ian

Geometriae Dedicata, 119(1) (pp. 91-104)

**The hyperbolic geometry of continued fractions**

**K**(1|*b*) (2006)nShort, Ian

Annales Academiae Scientiarum Fennicae Mathematica, 31(2) (pp. 315-327)

**A counterexample to a continued fraction conjecture (2006)**

Short, Ian

Proceedings of the Edinburgh Mathematical Society. Series II, 49(3) (pp. 735-737)

### Authored books

**Reversibility in Dynamics and Group Theory (2015-05-31)**

O'Farrell, Anthony G. and Short, Ian

London Mathematical Society Lecture Note Series

ISBN : 9781107442887 | Publisher : Cambridge University Press | Published : Cambridge

### Conference items

**Even-integer continued fractions and the Farey tree (2014)**

Short, Ian and Walker, Mairi

In : SIGMAP 2014 (7 Jul 2014-11 July 2014, West Malvern, UK)