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Pure Mathematics

A research group of the Department of Mathematical Sciences.

Research Areas

• Algebraic geometry - cycles on algebraic surfaces; vector bundles
• Arithmetic - modular forms; L-functions; K-theory; Galois modules
• Differential geometry - minimal immersions; variational problems

Staff

Academic Staff

• Prof Victor Abrashkin
• Dr Dzmitry Badziahin
• Dr Anna Felikson
• Dr Jens Funke
• Dr Herbert Gangl
• Dr Wilhelm Klingenberg
• Dr Vitaliy Kurlin
• Dr Andrew Lobb
• Prof John Parker
• Dr Norbert Peyerimhoff
• Dr Olaf Post
• Dr Dirk Schuetz
• Dr Alexander Stasinski
• Dr Fredrik Stromberg
• Dr Pavel Tumarkin
• Professor Thomas Ward

Teaching Staff

• Dr Vernon Armitage
• Dr John Bolton
• Dr Sophia Darwin
• Dr Daniel Evans
• Dr Cherry Kearton

Research Student

• Mr Jonathan Crawford
• Mr Daniel Jones
• Mrs Zakiah Kalantan
• Mr Keith Mccabe
• Mr John Mcleod
• Miss Marjan Safi-Samghabadi
• Mr Luke Stanbra
• Mr Ramon Vera

Publications by staff in this group

Journal papers: academic

• 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.
• Flatters, A & Ward, T (2011). A polynomial Zsigmondy theorem. Journal of algebra 343(1): 138.
• 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.
• 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.

Edited works: conference proceedings

• Parker, John R (2012). Traces in complex hyperbolic geometry. Geometry, Topology and Dynamics of Character Varieties, National University of Singapore, World Scientific.
• Parker, John R. & Platis, Ioannis D. (2010). Complex hyperbolic quasi-Fuchsian groups. Geometry of Riemann Surfaces, Anogia, Crete, Greece, Cambridge University Press.
• Parker, John R. (2009). Complex hyperbolic lattices. Discrete groups and geometric structures, Kortrijk, Belgium, American Mathematical Society.
• 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.