Publications

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

 

Preprints

Blaschke products and domains of ellipticity (pdf).

 

Papers

• 26. On quasiregular linearizers (pdf) with D. Macclure, to appear in Comp. Meth. Func. Th.

• 25. Julia sets and wild Cantor sets (pdf) with J.-M. Wu, to appear in Geometriae Dedicata.

• 24. Superattracting fixed points of quasiregular mappings (pdf) with D.A.Nicks, to appear in Ergodic Theory and Dynamical Systems.

• 23. Dynamics of mappings with constant complex dilatation (pdf) with R.Fryer, to appear in Ergodic Theory and Dynamical Systems.

• 22. The fast escaping set for quasiregular mappings (pdf) with W.Bergweiler and D.Drasin, Anal. Math. Phys. 4 (2014), 83-98.

• 21. The Julia set and the fast escaping set of a quasiregular mapping (pdf) with W.Bergweiler and D.A.Nicks, Comp. Meth. Func. Th., 14, no.2 (2014), 209-218.

• 20. Poincare linearizers in higher dimensions (pdf), to appear in Proc. Amer. Math. Soc.

• 19. The moduli space of Riemann surfaces of large genus (pdf) with J.Kahn and V.Markovic, Geometric and Functional Analysis, 23, no.3 (2013), 867-887.

• 18. Chaotic dynamics of a quasiregular sine mapping (pdf) with D.A.Nicks, J.Difference Equ. Appl., 19, no.8 (2013), 1353-1360.

• 17. On Bottcher coordinates and quasiregular maps (pdf) with R.Fryer, Contemp. Math., 575, volume title: Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces (2012), 53-76.

• 16. Decomposing diffeomorphisms of the sphere (pdf) with V.Markovic, Bull. London Math. Soc., 44, no.3 (2012), 599-609.

• 15. Iteration of quasiregular tangent functions in three dimensions (pdf) with D.A.Nicks, Conform. Geom. Dyn., 16 (2012), 1-21. See this gallery for related images.

• 14. Julia sets of uniformly quasiregular mappings are uniformly perfect (pdf) with D.A.Nicks, Math. Proc. Cam. Phil. Soc., 151, no.3 (2011), 541-550.

• 13. Quasiregular dynamics on the n-sphere (pdf) with D.A.Nicks, Ergodic Theory and Dynamical Systems, 31 (2011), 23-31. Also on the arxiv.

• 12. Quasiregular mappings of polynomial type in R^2 (pdf) with D.Goodman, Conform. Geom. Dyn., 14 (2010), 322-336.

• 11. On Asymptotic Teichmüller space (pdf), Trans. Amer. Math. Soc., 362 (2010), 2507-2523.

• 10. Nonvanishing derivatives and the MacLane class A (pdf) with J.K.Langley and J.Meyer, Illinois J. Math., 53 (2009) 379-390.

• 9. Integer points of analytic functions in a half-plane (pdf) with J.K.Langley, Proc. Edin. Math. Soc., 52, no.3 (2009) 619-630.

• 8. Meromorphic compositions and target functions (pdf) with J.K.Langley, Ann. Acad. Sci. Fenn., 34 (2009), 615-636.

• 7. Slowly growing meromorphic functions and the zeros of differences (pdf) with J.K.Langley and J.Meyer, Math. Proc. R. Ir. Acad., 109A(2) (2009), 147-154.

• 6. Infinite dimensional Teichmüller spaces (pdf) 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 (pdf) with W.Bergweiler, J.K.Langley and J.Meyer, Proc. Amer. Math. Soc., 137 (2009) 641-651. Also on the arxiv.

• 4. On Bank-Laine functions (pdf), Computational Methods and Function Theory, 9, (2009) 227-238.

• 3. Gaussian integer points of functions analytic in a half-plane (pdf), Math. Proc. Cam. Phil. Soc., 145, no.2 (2008), 257-272.

• 2. Local rigidity of infinite dimensional Teichmüller spaces (pdf) J. London Math. Soc., (2) 74 (2006) 26-40.

• 1. On the zeros of functions in the Bers space (pdf) Publications de l'Institut Mathématique, Nouvelle série, tome 75, (89) (2004) 185-197 (with V.Markovic). (Note that the proof of Theorem 4.5 can charitably be called unclear. Refer to my thesis below, pages 114-120, 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 (pdf) 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 Quasiregular Poincare linearizers, UIUC, October 2013, and Graduate Center, NY, February 2014.

Slides from a mini-course on Infinite dimensional Teichmueller spaces, Morelia, Mexico, July/August 2013.

Talk on decomposing diffeomorphisms of the sphere, Ahlfors-Bers 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 Urbana-Champaign, 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 q-differences 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 Bi-Lipschitz mappings of Teichmüller spaces, given at Ahlfors-Bers Colloquium, Rutgers University, Newark, US, May 2008.

   

Others

University of Cambridge Part 3 Essay (pdf) on Bloch functions, assessed by Dr. Keith Carne.

Jordan Normal Form (pdf) is an article I wrote to help Warwick undergraduates find the Jordan Normal Form of 2x2 and 3x3 matrices.