

Publications The versions on this page are generally early versions which come with the usual health warning with regards to typos and errors. See the relevant journal for the final version.


Preprints • Attractor sets and Julia sets in low dimensions • Quasiconformality and hyperbolic skew, with C. Ackermann • On simultaneous linearization, with D. Macclure • Spiders' webs of doughnuts, with D. Stoertz • The orbits of generalized derivatives, with B. Wallis


Papers • 33. Quasiregular semigroups with examples, to appear in Discrete Contin. Dyn. Syst. • 32. Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings, with D. Macclure, to appear in Journal d'Analyse Mathematique. • 31. Epicycloids and Blaschke products, with C. Cao and Z. Ye, Journal of Difference Equations and Applications, 23, no.9 (2017), 15841596. • 30. On infinitesimal Strebel points, Kodai Math. J., 40, no.3 (2017), 553561. • 29. On the infinitesimal space of uqr mappings, with D. Macclure, J. Waterman and S. Wesley, Journal of Analysis, Volume 24, Issue 1 (2016), 6781. • 28. Fixed curves near fixed points, Illinois J. Math, 59, no.1 (2016), 189217. • 27. Superattracting fixed points of quasiregular mappings with D.A.Nicks, Ergodic Theory and Dynamical Systems, 36, no.3, (2016), 781793. • 26. Dynamics of mappings with constant complex dilatation with R.Fryer, Ergodic Theory and Dynamical Systems, 36, no.2 (2016), 514549. • 25. Unicritical Blaschke products and domains of ellipticity, Qual. Th. Dyn. Sys., 14, no.1 (2015), 2538. • 24. On quasiregular linearizers with D. Macclure, Comp. Meth. Func. Th., 15, no.2 (2015), 263276. • 23. Julia sets and wild Cantor sets with J.M. Wu, Geometriae Dedicata, 174, no.1 (2015), 169176. • 22. Poincare linearizers in higher dimensions, Proc. Amer. Math. Soc., 143 (2015), 25432557. • 21. The fast escaping set for quasiregular mappings with W.Bergweiler and D.Drasin, Anal. Math. Phys. 4 (2014), 8398. • 20. The Julia set and the fast escaping set of a quasiregular mapping with W.Bergweiler and D.A.Nicks, Comp. Meth. Func. Th., 14, no.2 (2014), 209218. • 19. The moduli space of Riemann surfaces of large genus with J.Kahn and V.Markovic, Geometric and Functional Analysis, 23, no.3 (2013), 867887. • 18. Chaotic dynamics of a quasiregular sine mapping with D.A.Nicks, J.Difference Equ. Appl., 19, no.8 (2013), 13531360. • 17. On Bottcher coordinates and quasiregular maps with R.Fryer, Contemp. Math., 575, volume title: Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces (2012), 5376. • 16. Decomposing diffeomorphisms of the sphere with V.Markovic, Bull. London Math. Soc., 44, no.3 (2012), 599609. • 15. Iteration of quasiregular tangent functions in three dimensions with D.A.Nicks, Conform. Geom. Dyn., 16 (2012), 121. See this gallery for related images. • 14. Julia sets of uniformly quasiregular mappings are uniformly perfect with D.A.Nicks, Math. Proc. Cam. Phil. Soc., 151, no.3 (2011), 541550. • 13. Quasiregular dynamics on the nsphere with D.A.Nicks, Ergodic Theory and Dynamical Systems, 31 (2011), 2331. Also on the arxiv. • 12. Quasiregular mappings of polynomial type in R^2 with D.Goodman, Conform. Geom. Dyn., 14 (2010), 322336. • 11. On Asymptotic Teichmüller space, Trans. Amer. Math. Soc., 362 (2010), 25072523. • 10. Nonvanishing derivatives and the MacLane class A with J.K.Langley and J.Meyer, Illinois J. Math., 53 (2009) 379390. • 9. Integer points of analytic functions in a halfplane with J.K.Langley, Proc. Edin. Math. Soc., 52, no.3 (2009) 619630. • 8. Meromorphic compositions and target functions with J.K.Langley, Ann. Acad. Sci. Fenn., 34 (2009), 615636. • 7. Slowly growing meromorphic functions and the zeros of differences with J.K.Langley and J.Meyer, Math. Proc. R. Ir. Acad., 109A(2) (2009), 147154. • 6. Infinite dimensional Teichmüller spaces with V.Markovic. A survey article in the Handbook of Teichmüller theory, Volume 2 by the European Mathematical Society. • 5. The escaping set of a quasiregular mapping with W.Bergweiler, J.K.Langley and J.Meyer, Proc. Amer. Math. Soc., 137 (2009) 641651. Also on the arxiv. • 4. On BankLaine functions, Computational Methods and Function Theory, 9, (2009) 227238. • 3. Gaussian integer points of functions analytic in a halfplane, Math. Proc. Cam. Phil. Soc., 145, no.2 (2008), 257272. • 2. Local rigidity of infinite dimensional Teichmüller spaces, J. London Math. Soc., (2) 74 (2006) 2640. • 1. On the zeros of functions in the Bers space (ps), Publications de l'Institut Mathématique, Nouvelle série, tome 75, (89) (2004) 185197 (with V.Markovic). (Note that the proof of Theorem 4.5 can charitably be called unclear. Refer to my thesis below, pages 114120, for a complete proof. Section 3.5 of my thesis gives a different proof of Theorem 4.5 using Teichmüller theory)


Thesis • My PhD Thesis entitled Local Rigidity of Infinite Dimensional Teichmüller Spaces, essentially a combination of my first two papers. 

Book • Alastair Fletcher & Vladimir Markovic: Quasiconformal Maps and Teichmüller Theory. Oxford Graduate Texts in Mathematics 11. Oxford University Press (2007). Perhaps you would like to read the preface with the list of contents?


Slides • Talk on Infinitesimal spaces, AMS Sectional meeting, Hunter College, NY, May 2017. • Talk on Quasiregular Poincare linearizers, UIUC, October 2013, and Graduate Center, NY, February 2014. • Slides from a minicourse on Infinite dimensional Teichmueller spaces, Morelia, Mexico, July/August 2013. • Talk on decomposing diffeomorphisms of the sphere, AhlforsBers Colloquium, Rice University, Houston, March 2011. • Talk on Quasiregular dynamics, at the Dynamics Seminar, University of Warwick, November 2009, an updated version of this talk at the Analysis Seminar, University of Glasgow, September 2009. The most recent version is this one given at the University of Illinois at UrbanaChampaign, May 2010. The accompanying pictures can be viewed here. • Talk on Asymptotic Teichmüller spaces, Summer school in Conformal Geometry and Potential Theory, NUI Maynooth, June 2009. • Talk on qdifferences and target functions, given at CMFT conference, Bilkent University, Ankara, Turkey, June 2009. • Talk on Escaping sets of quasiregular mappings, given at the Aspects of Transcendental Dynamics meeting at Jacobs University, Bremen, Germany, June 2008. • Talk on BiLipschitz mappings of Teichmüller spaces, given at AhlforsBers Colloquium, Rutgers University, Newark, US, May 2008. 

Others • University of Cambridge Part 3 Essay on Bloch functions, assessed by Dr. Keith Carne. • Jordan Normal Form is an article I wrote to help Warwick undergraduates find the Jordan Normal Form of 2x2 and 3x3 matrices. 