Conformal Geometry and its Applications

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Conformal Geometry and its Applications

a thematic programme of the

New Zealand Institute of Mathematics and Its Applications

January - March and July - December 2008


Themes and Aims

(i) Conformal and hyperbolic geometry: conformally compact structures, hyperbolic and, more generally, asymptotically hyperbolic Poincare-Einstein metrics; conformally flat manifolds via differential geometry and via Kleinian groups – exploring links; geometric analysis.

(ii) Symmetries and natural geometric equations: approaches to overdetermined PDE and elliptic operators by prolonged systems and symmetries; geometric structure of DEs and PDEs – links to conformal and related geometries; applications in hyperbolic geometry, Riemannian geometry and conformal geometry; applications in other areas – including discretisation for numerical calculations and applications in physics

(iii) Invariants and applications: general theory of invariants of geometric structures – especially conformal and hyperbolic structures and links to topological data; scattering and asymptotic invariants of conformally compact structures; invariants of DE and PDE – invariants giving coordinate independent characterisations of DE/PDE, invariants obstructing solutions.

(iv) Nonlinear elasticity and materials science: the governing equations of nonlinear elasticity and (theoretical) materials science and those of conformal geometry are basically the same. Key problems in materials science are bridging length structures and analysing fractal microstructures. Conformal geometry would seem to supply the tools for this. We intend to explore connections between our knowledge of these fields and those of more applied researchers in these areas.

NZIMA Fellows

  • Research Fellow: n/a Rm n/a, Ext n/a, homepage University of Auckland
  • NZIMA programme scholar: Haydn Cooper, PhD research into computational conformal geometry, Massey University, Albany


  • Programme Director: A. Rod Gover Rm 303.427, Ext 88792, homepage, Department of Mathematics, University of Auckland
  • Programme Director Gaven Martin, Room 3.23, Phone +64 9 414-0800 ext. 41124, Institute of Information and Mathematical Sciences, Massey University, Albany, Auckland,

Key Activities

NZMRI Summer instructional workshop

Conformal geometry and geometric approaches to PDE

Research workshop

Parabolic Geometry and PDE, 4-8 August 2008, Room 222, Department of Mathematics, University of Auckland.

Focussed Research Period

"Parabolic geometry, PDE and prolonged systems", 20 July - 10 September 2008, University of Auckland

The aim of this period is to progress several closely related areas of Geometry and the geometric approaches to PDE. The activity will comprise informal seminars and working groups. involving New Zealand and international participants. Over this period there will be a concentration of extended visits by international participants in the programme.
Themes: Prolonged differential systems; Higher symmetries of PDE and their applications; Geometric PDE; Parabolic geometry (including conformal geometry, CR geometry and related structures); Hyperbolic Geometry. A key focus will be to explore the interplay between parabolic geometry (including conformal, CR, projective and related structures) and prolonged differential systems.


Geometry and analysis working group. Talks and meetings are usually Fridays at 9:30am in 401, Department of Mathematics, University of Auckland

Students associated with the Programme

  • Niels Bernhardt, University of Auckland
  • Howard Cohl, University of Auckland
  • Luke Fullard, Massey University, Palmerston North
  • Maarten Jordens, New Zealand Institute of Advanced Study
  • Hyukjoon Kang, Massey University
  • Geon Oh, University of Auckland
  • Mathew Randall, University of Auckland
  • Callum Sleigh, University of Auckland
  • Qingxiang Zhang, Massey University


  • Kari Astala, (Acad. Prof.) University of Helsinki
  • Ian Agol, (Prof.), UC Berkeley
  • Paul Baird, (Prof.), Departement de Mathematiques, University of Brest
  • Robert Bartnik, (Dr.), Monash University
  • Robert Bryant, (Prof), MSRI Berkeley & Duke University
  • Stuart Armstrong (Dr.), Erwin Schroedinger International Institute for Mathematical Physics, Vienna
  • Ian Benn, (Dr.) University of Newcastle, Australia
  • Andreas Cap, (Prof.), Erwin Schroedinger Institute & University of Vienna
  • Alex Castro, (Mr.), U of California at Santa Cruz
  • Alice Chang, (Prof.), Princeton University
  • Michael Eastwood, (Prof.), University of Adelaide
  • Robin Graham, (Prof.), University of Washington
  • Colin Guilarmou, (Prof.), University of Nice
  • Matthias Hammerl, University of Vienna
  • Chong-Kyu Han, (Prof.) Seoul National University
  • Oussama Hijazi, (Prof.), Institut Elie Cartan de Mathmatiques, University of Nancy
  • Kengo Hirachi, (Prof.), University of Tokyo
  • Jonathan Kress, (Dr.) UNSW, Sydney
  • Jens Kroeske, (Mr.) University of Adelaide
  • Claude LeBrun, (Prof.) Stony Brook, SUNY
  • Felipe Leitner, (Dr.) University of Stuttgart
  • Pengzi Miao, (Dr.) Monash University
  • Willard Miller, Jr. (Prof.), University of Minnesota
  • Katharina Neusser, (Dr.) University of Vienna
  • Eugene Poletsky (Prof.), Syracuse University, New York
  • Josef Silhan, (Dr.) Masaryk University and International School for Advanced Studies, Trieste
  • Jan Slovak, (Prof.), Masaryk University
  • Petr Somberg, (Prof.), Charles University, Prague
  • Vladimir Soucek, (Prof.), Charles University, Prague
  • Neil Trudinger, (Prof.), Australian National University
  • Paul Yang, (Prof.), Princeton University
  • Keizo Yamaguchi, (Prof.), Hokkaido University

New Zealand Participants

  • Christopher Atkin, (Prof.), Victoria University, Wellington
  • Vaughan Jones (Dist. Prof.), (Berkeley University and University of Auckland)
  • Christopher Atkin, (Prof.), Victoria University, Wellington
  • Samuel Dillon, (Mr.), Massey University
  • Jörg Frauendiener, (Prof.), University of Otago
  • David Gauld, (Prof.), University of Auckland
  • Mark Hickman, (Dr.), University of Canterbury
  • Ernie Kalnins, (Prof.), Waikato University
  • Gerrard Liddell, (Dr.), Otago University
  • Stephen Marsland, (Dr.), Massey University, Palmerston North
  • Mike Meylan, (Dr.), University of Auckland
  • Bruce van Brunt, (Dr.) Massey University, Palmerston North
  • Shixiao Wang, (Dr.), University of Auckland
  • Matt Visser, (Prof.), Victoria University, Wellington

Related activities

Geometry and Analysis Working Group and Seminars

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