Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Email and Telephone Directory

Staff Profile

John Parker, PhD University of Cambridge

ORCID profile

Personal web page

Head of Department, Professor, Geometry in the Department of Mathematical Sciences

Contact John Parker (email at j.r.parker@durham.ac.uk)

Research Groups

Department of Mathematical Sciences

  • Pure Mathematics
  • Pure Mathematics: Geometry

Research Interests

  • Discrete groups
  • Hyperbolic geometry

Publications

Chapter in book

  • Parker, John R & Series, Caroline (2004). The mapping class group of the twice punctured torus. In Groups: Topological, Combinatorial and Arithmetic Aspects. Mueller, Thomas W. Cambridge University Press. 311: 405-486.
  • Menzel, Christof. & Parker, John R. (2003). Pseudo-Anosov diffeomorphisms of the twice punctured torus. In Recent Advances in Group Theory and Low-Dimensional Topology. Cho, Jung Rae. & Mennicke, Jens. Heldermann Verlag. 27: 141-154.
  • Parker, John R. (2003). Tetrahedral decomposition of punctured torus bundles. In Kleinian Groups and Hyperbolic 3-Manifolds. Komori, Yohei., Markovic, Vladimir, & Series, Caroline. Cambridge University Press. 299: 275-291.
  • Parker, John R. & Parkkonen, Jouni (1998). Coordinates for quasi-Fuchsian punctured torus space. In The Epstein Birthday Schrift. Geometry and Topology Monographs. 1: 451-478.

Journal Article

  • Kneiper, Gerhard, Parker, John R & Peyerimhoff, Norbert (2020). Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces. Differential Geometry and its Applications 69: 101605.
  • Deraux, Martin, Parker, John R & Paupert, Julien (2020). New non-arithmetic complex hyperbolic lattices II. Michigan Mathematical Journal
  • Monaghan, Andrew, Parker, John R. & Pratoussevitch, Anna (2019). Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type [m_1,m_2,0]. Journal of the London Mathematical Society 100(2): 545-567.
  • Parker, John R, Peyerimhoff, Norbert & Siburg, Karl Friedrich (2018). Minimizing length of billiard trajectories in hyperbolic polygons. Conformal Geometry and Dynamics 22: 315-332.
  • Parker, John R. (2018). On cusp regions associated to screw-parabolic maps. Geometriae Dedicata 192(1): 267-294.
  • Cao, Wensheng & Parker, John R. (2018). Shimizu’s Lemma for Quaternionic Hyperbolic Space. Computational Methods and Function Theory 18(1): 159-191.
  • Parker, John R. & Will, Pierre (2017). A complex hyperbolic Riley slice. Geometry & Topology 21(6): 3391-3451.
  • Parker, John R. & Sun, Lijie (2017). Complex Hyperbolic Triangle Groups with 2-fold Symmetry. Proceedings of the International Geometry Center 10(1): 1-21.
  • Cano, Angel, Parker, John R. & Seade, José (2016). Action of R-Fuchsian groups on CP2. The Asian Journal of Mathematics 20(3): 449-474.
  • Parker, John R., Wang, Jieyan & Xie, Baohua (2016). Complex hyperbolic (3,3,n)-triangle groups. Pacific Journal of Mathematics 280(2): 433-453.
  • Deraux, Martin, Parker, John R. & Paupert, Julien (2016). New non-arithmetic complex hyperbolic lattices. Inventiones Mathematicae 203(3): 681-771.
  • Boadi, Richard K & Parker, John R (2015). Mostow's lattices and cone metrics on the sphere. Advances in Geometry 15(1): 27-53.
  • Gongopadhyay, Krishnendu, Parker, John R. & Parsad, Shiv (2015). On the classification of unitary matrices. Osaka Journal of Mathematics 52(4): 959-993.
  • Gongopadhyay, Krishnendu & Parker, John R (2013). Reversible complex hyperbolic isometries. Linear Algebra and its Applications 438(6): 2728-2739.
  • Kamiya, Shigeyasu, Parker, John R. & Thompson, James M. (2012). Non-Discrete Complex Hyperbolic Triangle Groups of Type (n,n,infinity;k). Canadian Mathematical Bulletin 55(2): 329-338.
  • Deraux, Martin, Parker, John R & Paupert, Julien (2011). Census of the complex hyperbolic sporadic triangle groups. Experimental Mathematics 20(4): 467-586.
  • Falbel,Elisha, Francsics,Gabor, Lax, Peter D & Parker, John R (2011). Generators of a Picard modular group in two complex dimensions. Proceedings of the American Mathematical Society 139: 2439-2447.
  • Cao, Wensheng. & Parker, John R. (2011). Jørgensen's inequality and collars in n-dimensional quaternionic hyperbolic space. Quarterly Journal of Mathematics 62(3): 523-543.
  • Falbel, Elisha, Francsics, Gabor & Parker, John R (2011). The geometry of the Gauss-Picard modular group. Mathematische Annalen 349(2): 459-508.
  • Kamiya, Shigeyasu, Parker, John R. & Thompson, James M. (2010). Notes on complex hyperbolic triangle groups. Conformal Geometry and Dynamics 14: 202-218.
  • Parker, John R. & Short, Ian. (2009). Conjugacy classification of quaternionic Moebius transformations. Computational Methods and Function Theory 9(1): 13-25.
  • Parker, John R. & Platis, Ioannis D. (2009). Global, geometrical coordinates on Falbel's cross-ratio variety. Canadian Mathematical Bulletin 52(2): 285-294.
  • Parker, John R. & Paupert, Julien (2009). Unfaithful complex hyperbolic triangle groups II: Higher order reflections. Pacific Journal of Mathematics 239(2): 357-389.
  • Parker,J.R. & Platis,I.D. (2008). Complex hyperbolic Fenchel-Nielsen coordinates. Topology 47(2): 101-135.
  • Kamiya,S. & Parker,J.R. (2008). Discrete subgroups of PU(2,1) with screw parabolic elements. Mathematical Proceedings of the Cambridge Philosophical Society 144(2): 443-455.
  • Parker, John R. (2008). Unfaithful complex hyperbolic triangle groups I: Involutions. Pacific Journal of Mathematics 238(1): 145-169.
  • Markham,Sarah. & Parker,John R. (2007). Jorgensen's inequality for metric spaces with applications to the octonions. Advances in Geometry 7: 19-38.
  • Parker, John R. (2006). Cone metrics on the sphere and Livné's lattices. Acta Mathematica 196(1): 1-64.
  • Parker, John R & Platis, Ioannis D (2006). Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space. Journal of Differential Geometry 73(2): 319-350.
  • Falbel, Elisha & Parker, John R (2006). The geometry of the Eisenstein-Picard modular group. Duke Mathematical Journal 131(2): 249-289.
  • Mednykh, Alexander D., Parker, John R. & Vesnin, Andrei Yu (2004). On hyperbolic polyhedra arising as convex cores of quasi-Fuchsian punctured torus groups. Boletin de la Sociedad Matematica Mexicana 10(3): 357-381.
  • Cao, Wensheng, Parker, John R. & Wang, Xiantao (2004). On the classification of quaternionic Moebius transformations. Mathematical Proceedings of the Cambridge Philosophical Society 137(2): 349-361.
  • Markham, Sarah. & Parker, John R. (2003). Collars in complex and quaternionic hyperbolic manifolds. Geometriae Dedicata 97: 199-213.
  • Gusevskii, Nikolay & Parker, John R. (2003). Complex hyperbolic quasi-Fuchsian groups and Toledo's invariant. Geometriae Dedicata 97: 151-185.
  • Kim, Inkang & Parker, John R (2003). Geometry of quaternionic hyperbolic manifolds. Mathematical Proceedings of the Cambridge Philosophical Society 135(2): 291-320.
  • Jiang, Yueping, Kamiya, Shigeyasu & Parker, John R (2003). Jorgensen's inequality for complex hyperbolic space. Geometriae Dedicata 97: 55-80.
  • Falbel, Elisha & Parker, John R. (2003). The moduli space of the modular group in complex hyperbolic geometry. Inventiones Mathematicae 152(1): 57-88.
  • Jiang, Yueping & Parker, John R. (2003). Uniform discreteness and Heisenberg scew motions. Mathematische Zeitschrift 243: 653-669.
  • Kamiya, Shigeyasu. & Parker, John R. (2002). On discrete subgroups of PU(1,2;C) with Heisenberg translations II. Revue Roumaine Mathematiques Pures et Appliquees 47(5-6): 689-695.
  • Parker, John R. & Stratmann, Bernd O. (2001). Kleinian groups with singly cusped parabolic fixed points. Kodai Mathematical Journal 24(2): 169-206.
  • Gusevskii, Nikolay & Parker, John R. (2000). Representations of free Fuchsian groups in complex hyperbolic space. Topology 39(1): 33-60.
  • Keen, Linda, Parker, John R. & Series, Caroline (1999). Combinatorics of simple closed curves on the twice punctured torus. Israel Journal of Mathematics 112: 29-60.
  • Parker, John R. (1998). On the volumes of cusped, complex hyperbolic manifolds and orbifolds. Duke Mathematical Journal 94(3): 433-464.
  • Parker, John R. (1997). Uniform discreteness and Heisenberg translations. Mathematische Zeitschrift 225: 484-505.
  • Parker, John R. & Series, Caroline. (1996). Bending Formulae for Convex Hull Boundaries. Journal d'Analyse Mathematique 67: 165-198.
  • Parker, John R. (1995). Dirichlet polyhedra for parabolic cyclic groups in complex hyperbolic space. Geometriae Dedicata 57(3): 223-234.
  • Parker, John R. (1995). Kleinian circle packings. Topology 34(3): 489-496.
  • McShane, Greg., Parker, John R. & Redfern, Ian (1994). Drawing Limit Sets of Kleinian Groups using Finite State Automata. Experimental Mathematics 3: 153-170.
  • Parker, John R. (1994). On Ford Isometric Spheres in Complex Hyperbolic Space. Mathematical Proceedings of the Cambridge Philosophical Society 115: 501-512.

Conference Paper

  • Parker, John R. & Will, Pierre (2015), Complex hyperbolic free groups with many parabolic elements, Contemporary Mathematics 639: Groups, Geometry and Dynamics. Almora, Uttarakhand, India, American Mathematical Society, 327-348.
  • Parker, John R. (2012), Traces in complex hyperbolic geometry, in Goldman, William M., Series, Caroline & Tan, Ser Peow eds, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 23: Geometry, Topology and Dynamics of Character Varieties. Singapore, World Scientific, Singapore, 191-245.
  • Parker, John R. & Platis, Ioannis D. (2010), Complex hyperbolic quasi-Fuchsian groups, in Gardiner, Frederick P. González-Diez, Gabino & Kourouniotis, Christos eds, 368: Geometry of Riemann Surfaces. Anogia, Crete, Greece, Cambridge University Press, Cambridge, 309-355.
  • Parker, John R. (2009), Complex hyperbolic lattices, in Dekimpe, Karel, Igodt, Paul & Valette, Alain eds, 501: Discrete groups and geometric structures. Kortrijk, Belgium, American Mathematical Society, Providence, R.I., 1-42.

Conference Proceeding

  • Armitage, J.Vernon. & Parker, John R. (2008). Jorgensen's inequality for non-Archimedean metric spaces. Geometry and Dynamics of Groups and Spaces In Memory of Alexander Reznikov, Bonn, Birkhauser.

Supervises