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Distinguished Professor Gaven Martin staff profile picture

Contact details +6492136148

Distinguished Professor Gaven Martin PhD

Professor

Doctoral Supervisor
New Zealand Institute for Advanced Study

Professional

Qualifications

  • Doctorate - The University of Michigan (1985)

Prizes and Awards

  • Fully supported visit for five weeks in June/July 2010. This developed research projects with a number of German based (and visiting) researchers in Geometry and Analysis. From: Hausdorff Institute of Mathematics - (2010)

Research Projects

Current Projects

Project Title: Modern Analysis and Geometry

Date Range: 2022 - 2025

Funding Body: Royal Society of New Zealand

Project Team:

Completed Projects

Project Title: Modern Analysis and Geometry

Date Range: 2019 - 2023

Funding Body: Royal Society of New Zealand

Project Team:

Project Title: Modern analysis and geometry

Date Range: 2016 - 2019

Funding Body: Royal Society of New Zealand

Project Team:

Project Title: Lineage selection and the evolution of cancer

Date Range: 2015 - 2019

Funding Body: Royal Society of New Zealand

Project Team:

Project Title: Modern analysis and Geometry

This proposal sits at the forefront of two central areas of modern mathematics; nonlinear analysis and low dimensional topology & geometry; unified by themes in conformal geometry and geometric function theory. We attack important longstanding problems with wide ranging applications. These include the classification of conformal dynamical systems on manifolds and their dynamically defined invariants. This project interacts with our novel results in geometric group theory. We investigate the structure and classification of arithmetic hyperbolic orbifolds extending our solution of Sigel's1945 problem by developing new methods to attack key problems in hyperbolic geometry.
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Date Range: 2013 - 2016

Funding Body: Marsden Fund - Full

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Project Title: Advances in scattering theory and solvable models

Contact with the external world takes place by detecting waves and particles scattered by objects in it; understanding this process is one of the most important tasks of physical and mathematical models. Classical schemes fail for operators with continuous spectrum (divergence of perturbation series). Typical problems include 1. Scattering of acoustic waves - Helmholtz resonator; 2. Scattering of electrons in quantum networks; 3. Plasma waves in electron channels: propagation and trapped modes. We develop innovative methods to solve these problems via fitting zero-range solvable models, intermediate operators, and nonlinear resonance duality. Applications in quantum networks and tomography are developed.
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Date Range: 2010 - 2013

Funding Body: Marsden Fund - Full

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Project Title: Proteins from pieces: subdomain assembly in the evolution of protein structure

Date Range: 2010 - 2012

Funding Body: Marsden Fund - Full

Project Team:

Project Title: Modern Analysis and Geometry

This research investigates two central areas of modern mathematics; nonlinear analysis and low dimensional topology linked by conformal geometry. These areas have undergone enormous growth due to a new understanding of their relevance and far reaching applications, and our research is helping to understand important and longstanding questions in these areas.
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Date Range: 2008 - 2013

Funding Body: Marsden Fund - Full

Project Team:

Research Outputs

Journal

Hashemi, M., & Martin, GJ. (2024). The Generic Failure of Lower-Semicontinuity for the Linear Distortion Functional. Computational Methods and Function Theory.
[Journal article]Authored by: Martin, G.
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Martin, G., & Yao, C. (2024). The Lp Teichmüller Theory: Existence and Regularity of Critical Points. Archive for Rational Mechanics and Analysis. 248(2)
[Journal article]Authored by: Martin, G.
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Martin, G., & Yao, C. (2023). Topological Regularity for Solutions to the Generalised Hopf Equation. Complex Analysis and Operator Theory. 17(6)
[Journal article]Authored by: Martin, G.
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Elzenaar, A., Martin, G., & Schillewaert, J. (2023). Approximations of the Riley slice. Expositiones Mathematicae. 41(1), 20-54
[Journal article]Authored by: Martin, G.
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Alaqad, H., Gong, J., & Martin, G. (2023). Chebyshev polynomials and inequalities for Kleinian groups. Communications in Contemporary Mathematics. 25(2)
[Journal article]Authored by: Martin, G.
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Martin, G., & Yao, C. (2022). Extremal mappings of finite distortion and the Radon–Riesz property. Revista Matematica Iberoamericana. 38(7), 2057-2068
[Journal article]Authored by: Martin, G.
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Martin, GJ., & Yao, C. (2022). The Teichmüller problem for Lp-means of distortion. Annales Fennici Mathematici. 47(2), 1099-1108
[Journal article]Authored by: Martin, G.
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Alaqad, H., Gong, J., & Martin, G. (2022). Projections in Moduli Spaces of the Kleinian Groups. Abstract and Applied Analysis. 2022
[Journal article]Authored by: Martin, G.
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Herron, DA., & Martin, GJ. (2022). Subharmonic functions, conformal metrics, and CAT(0). Complex Analysis and its Synergies. 8(1)
[Journal article]Authored by: Martin, G.
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Martin, G., & Yao, C. (2022). Higher regularity and uniqueness for inner variational equations. Calculus of Variations and Partial Differential Equations. 61(1)
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2021). SUPER REGULARITY FOR BELTRAMI SYSTEMS. Annales Fennici Mathematici. 46(1), 59-65
[Journal article]Authored by: Martin, G.
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Martin, G., & Yao, C. (2021). Non-variational extrema of exponential Teichmüller spaces. Complex Analysis and its Synergies. 7(3-4)
[Journal article]Authored by: Martin, G.
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Iwaniec, T., Martin, G., & Onninen, J. (2021). Energy-minimal principles in geometric function theory. New Zealand Journal of Mathematics. 52, 605-642
[Journal article]Authored by: Martin, G.
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Martin, G., & Onninen, J. (2021). Pekka Koskela. Complex Analysis and its Synergies. 7(3-4)
[Journal article]Authored by: Martin, G.
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Liu, T., & Martin, G. (2020). K-Initialization-Similarity Clustering Algorithm. IEEE Intelligent Informatics Bulletin. 20(1), 9-16 Retrieved from https://www.comp.hkbu.edu.hk/~cib/2020/Article1.pdf
[Journal article]Authored by: Liu, T., Martin, G.
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Martin, GJ. (2021). Nondiscrete parabolic characters of the free group F<inf>2</inf>: supergroup density and Nielsen classes in the complement of the Riley slice. Journal of the London Mathematical Society. 103(4), 1402-1414
[Journal article]Authored by: Martin, G.
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Liu, T., Martin, G., Zhu, YX., Peng, L., & Li, L. (2020). Joint Robust Multi-view Spectral Clustering. Neural Processing Letters. 52(3), 1843-1862
[Journal article]Authored by: Liu, T., Martin, G.
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Liu, T., & Martin, G. (2020). Joint Feature Selection with Dynamic Spectral Clustering. Neural Processing Letters. 52(3), 1745-1763
[Journal article]Authored by: Liu, T., Martin, G.
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Martin, G., & O'Brien, G. (2019). Random möbius groups, I: Random subgroups of PSL(2,R). Pacific Journal of Mathematics. 303(2), 669-701
[Journal article]Authored by: Martin, G.
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Martin, G. (2020). Random lattices, punctured tori and the teichmüller distribution. Proceedings of the American Mathematical Society. 148(1), 289-300
[Journal article]Authored by: Martin, G.
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Hinkkanen, A., & Martin, G. (2020). Quasiregular Families Bounded in L<sup>p</sup> and Elliptic Estimates. Journal of Geometric Analysis. 30(2), 1627-1636
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2019). Random ideal hyperbolic quadrilaterals, the cross ratio distribution and punctured tori. Journal of the London Mathematical Society. 100(3), 851-870
[Journal article]Authored by: Martin, G.
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Martin, G., O’Brien, G., & Yamashita, Y. (2020). Random Kleinian Groups, II Two Parabolic Generators. Experimental Mathematics. 29(4), 443-451
[Journal article]Authored by: Martin, G.
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Klén, R., & Martin, G. (2017). Distortion and topology. Journal d'Analyse Mathematique. 133(1), 229-251
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2016). Siegel’s problem in three dimensions. Notices of the American Mathematical Society. 63(11), 1244-1247
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2016). Quasicircles as equipotential lines, homotopy classes and geodesics. Bulletin of the London Mathematical Society. 48(4), 648-656
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2016). Harmonic degree 1 maps are diffeomorphisms: Lewy’s theorem for curved metrics. Transactions of the American Mathematical Society. 368(1), 647-658
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2015). Stream lines, quasilines and holomorphic motions. Complex Analysis and its Synergies. 1(1)
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2015). Stream lines, quasilines and holomorphic motions. Complex Analysis and Synergys. 1(5), 1-8 Retrieved from https://casjournal.springeropen.com/articles/10.1186/s40627-015-0003-5
[Journal article]Authored by: Martin, G.
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Danieli, C., Rayanov, K., Pavlov, B., Martin, G., & Flach, S. (2015). Approximating metal-insulator transitions. International Journal of Modern Physics B. 29(6)
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2015). The tension equation with holomorphic coefficients, harmonic mappings and rigidity. Complex Variables and Elliptic Equations. 60(8), 1159-1167
[Journal article]Authored by: Martin, G.
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Adamyan, VM., Martin, GJ., & Pavlov, BS. (2014). Local Inverse Scattering Problem as a Tool of Perturbation Analysis for Resonance Systems. Advances in the Mathematical Sciences, Translations: American Mathematical Society Translations. 233, 12-38
[Journal article]Authored by: Martin, G.
Martin, GJ. (2014). Fred Gehring’s Mathematics. Computational Methods and Function Theory. 14(2-3), 177-193
[Journal article]Authored by: Martin, G.
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Iwaniec, T., Martin, G., & Onninen, J. (2014). On Minimisers of L<sup>p</sup>-mean Distortion. Computational Methods and Function Theory. 14(2-3), 399-416
[Journal article]Authored by: Martin, G.
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Goncharov, L., Yafyasov, A., Pavlov, BS., & Martin, GJ. (2014). The dispersion functions for quasi-2D periodic lattices via Dirichlet-to-Neumann map. Journal of Physics: Conference Series. 490(1)
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2013). Holomorphic motions and quasicircles. Proceedings of the American Mathematical Society. 141(11), 3911-3918
[Journal article]Authored by: Martin, G.
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Bagraev, NT., Martin, GJ., Pavlov, BS., Yafyasov, AM., Goncharov, LI., & Zubkova, AV. (2012). The dispersion function of a quasi two-dimensional periodic sandwich using a dirichlet-to-neumann map. Civil-Comp Proceedings. 99
[Journal article]Authored by: Martin, G.
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Marshall, TH., & Martin, GJ. (2012). Minimal co-volume hyperbolic lattices, II: Simple torsion in a Kleinian group. Annals of Mathematics. 176(1), 261-301
[Journal article]Authored by: Martin, G.
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Martin, GJ., & McKubre-Jordens, M. (2012). Deformations with smallest weighted L <sup>p</sup> average distortion and nitsche-type phenomena. Journal of the London Mathematical Society. 85(2), 282-300
[Journal article]Authored by: Martin, G.
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Martin, GJ., Pavlov, B., Ivlev, I., & Petrova, L. (2011). Solvable model of a localized boundary stress on the tectonic plate with dissipative boundary conditions. CoE Lecture Notes. 32, 51-55
[Journal article]Authored by: Martin, G.
Martin, G. (2011). A paper by S. K. Donaldson and D. P. Sullivan. REVISTA MATEMATICA IBEROAMERICANA. , 225-+
[Journal article]Authored by: Martin, G.
Pavlov, BS., Bagraev, N., Martin, G., & Yafyasov, A. (2011). Landau-Zener Effect for a quasi-2D periodic sandwich. Nanosystems:Physics,Chemistry,Mathematics. 2(4), 32-50
[Journal article]Authored by: Martin, G.
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Maclachlan, C., & Martin, GJ. (2011). The (6, p)-arithmetic hyperbolic lattices in dimension 3. Pure and Applied Mathematics Quarterly. 7(2), 365-382
[Journal article]Authored by: Martin, G.
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Bonfert-Taylor, P., Martin, G., Reid, AW., & Taylor, EC. (2011). Teichmüller mappings, quasiconformal homogeneity, and non-amenable covers of Riemann surfaces. Pure and Applied Mathematics Quarterly. 7(2), 455-468
[Journal article]Authored by: Martin, G.
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Martin, G., & Peltonen, K. (2010). Stöilow factorization for quasiregular mappings in all dimensions. Proceedings of the American Mathematical Society. 138(1), 147-151
[Journal article]Authored by: Martin, G.
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Astala, K., Iwaniec, T., & Martin, G. (2010). Deformations of annuli with smallest mean distortion. Archive for Rational Mechanics and Analysis. 195(3), 899-921
[Journal article]Authored by: Martin, G.
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Bridson, MR., Groves, D., Hillman, JA., & Martin, GJ. (2010). Cofinitely Hopfian groups, open mappings and knot complements. Groups, Geometry, and Dynamics. 4(4), 693-707
[Journal article]Authored by: Martin, G.
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Bonfert-Taylor, P., Canary, RD., Martin, G., Taylor, EC., & Wolf, M. (2010). Ambient quasiconformal homogeneity of planar domains. Annales Academiae Scientiarum Fennicae Mathematica. 35(1), 275-283
[Journal article]Authored by: Martin, G.
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Martin, G., & Peltonen, K. (2010). STOILOW FACTORIZATION FOR QUASIREGULAR MAPPINGS IN ALL DIMENSIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 138(1), 147-151
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2009). Aspects of quasiconformal homogeneity. New Zealand Journal of Mathematics. 39, 117-132
[Journal article]Authored by: Martin, G.
Gehring, FW., & Martin, GJ. (2009). Minimal co-volume hyperbolic lattices, I: The spherical points of a Kleinian group. Annals of Mathematics. 170(1), 123-161
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2009). The Teichmüller problem for mean distortion. Annales Academiae Scientiarum Fennicae Mathematica. 34(1), 233-247
[Journal article]Authored by: Martin, G.
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Brüning, J., Martin, G., & Pavlov, B. (2009). Calculation of the Kirchhoff coefficients for the Helmholtz resonator. Russian Journal of Mathematical Physics. 16(2), 188-207
[Journal article]Authored by: Martin, G.
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Iwaniec, T., Martin, G., & Sbordone, C. (2009). L<sup>P</sup>-integrability &amp; weak type L<sup>2</sup>-estimates for the gradient of harmonic mappings of D. Discrete and Continuous Dynamical Systems - Series B. 11(1), 145-152
[Journal article]Authored by: Martin, G.
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Astala, K., Iwaniec, T., & Martin, G. (2008). Monotone maps of Rn are quasiconformal. Methods and Applications of Analysis. 15(1), 31-37
[Journal article]Authored by: Martin, G.
Iwaniec, T., & Martin, G. (2008). The Beltrami equation. Memoirs of the American Mathematical Society. 191(893), 1-92
[Journal article]Authored by: Martin, G.
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Bridson, M., Hinkkanen, A., & Martin, G. (2007). Quasiregular self-mappings of manifolds and word hyperbolic groups. Compositio Mathematica. 143(6), 1613-1622
[Journal article]Authored by: Martin, G.
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Conder, M., Martin, G., & Torstensson, A. (2006). Maximal symmetry groups of hyperbolic 3-manifolds. New Zealand Journal of Mathematics. 35(1), 37-62
[Journal article]Authored by: Martin, G.
Bonfert Taylor, P., & Martin, G. (2006). Quasiconformal groups with small dilatation. Complex Variables and Elliptic Equations. 51(2), 165-179
[Journal article]Authored by: Martin, G.
Hinkkanen, A., & Martin, G. (2006). Limit functions for convergence groups and uniformly quasiregular maps. Journal of the London Mathematical Society. 73(3), 716-726
[Journal article]Authored by: Martin, G.
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Martin, G., Mayer, V., & Peltonen, K. (2006). The generalized Lichnerowicz problem: Uniformly quasiregular mappings and space forms. Proceedings of the American Mathematical Society. 134(7), 2091-2097
[Journal article]Authored by: Martin, G.
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Astala, K., Iwaniec, T., & Martin, G. (2006). Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane. Journal fur die Reine und Angewandte Mathematik. (591), 49-74
[Journal article]Authored by: Martin, G.
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Bonfert-Taylor, P., Canary, RD., Martin, G., & Taylor, E. (2005). Quasiconformal homogeneity of hyperbolic manifolds. Mathematische Annalen. 331(2), 281-295
[Journal article]Authored by: Martin, G.
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Bonfert-Taylor, P., & Martin, G. (2005). Quasiconformal groups of compact type. Revista Matematica Iberoamericana. 21(3), 997-1012
[Journal article]Authored by: Martin, G.
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Astala, K., Iwaniec, T., Martin, GJ., & Onninen, J. (2005). Extremal mappings of finite distortion. Proceedings of the London Mathematical Society. 91(3), 655-702
[Journal article]Authored by: Martin, G.
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Marshall, TH., & Martin, GJ. (2005). Cylinder and horoball packing in hyperbolic space. Annales Academiae Scientiarum Fennicae Mathematica. 30(1), 3-48
[Journal article]Authored by: Martin, G.
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Hinkkanen, A., Martin, GJ., & Mayer, V. (2004). Local dynamics of uniformly quasiregular mappings. Mathematica Scandinavica. 95(1), 80-100
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2004). Extending rational maps. Conformal Geometry and Dynamics. 8(7), 158-166
[Journal article]Authored by: Martin, G.
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Maclachlan, C., & Martin, GJ. (2003). All kleinian groups with two elliptic generators whose commutator is elliptic. Mathematical Proceedings of the Cambridge Philosophical Society. 135(3), 413-420
[Journal article]Authored by: Martin, G.
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Iwaniec, T., Koskela, P., Martin, G., & Sbordone, C. (2003). Mappings of finite distortion: L<sup>n</sup> log<sup>伪</sup> L-integrability. Journal of the London Mathematical Society. 67(1), 123-136
[Journal article]Authored by: Martin, G.
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Marshall, TH., & Martin, GJ. (2003). Packing strips in the hyperbolic plane. Proceedings of the Edinburgh Mathematical Society. 46(1), 67-73
[Journal article]Authored by: Martin, G.
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Martin, GJ., & Mayer, V. (2003). Rigidity in holomorphic and quasiregular dynamics. Transactions of the American Mathematical Society. 355(11), 4349-4363
[Journal article]Authored by: Martin, G.
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Marshall, TH., & Martin, GJ. (2003). Volumes of hyperbolic 3-manifolds. Notes on a paper of gabai, meyerhoff, and milley. Conformal Geometry and Dynamics. 7(3), 34-48
[Journal article]Authored by: Martin, G.
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Conder, MDE., Maclachlan, C., Martin, GJ., & O'Brien, EA. (2002). 2-generator arithmetic Kleinian groups III. Mathematica Scandinavica. 90(2), 161-179
[Journal article]Authored by: Martin, G.
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Martin, GJ. (2002). Analytic continuation for Beltrami systems, Siegel's theorem for UQR maps, and the Hilbert-Smith conjecture. Mathematische Annalen. 324(2), 329-340
[Journal article]Authored by: Martin, G.
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Iwaniec, T., & Martin, G. (2002). Squeezing the Sierpi艅ski sponge. Studia Mathematica. 149(2), 133-145
[Journal article]Authored by: Martin, G.
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Iwaniec, T., Koskela, P., & Martin, G. (2002). Mappings of BMO-distortion and Beltrami-type operators. Journal d'Analyse Mathematique. 88, 337-381
[Journal article]Authored by: Martin, G.
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Maclachlan, C., & Martin, GJ. (2001). The non-compact arithmetic generalised triangle groups. Topology. 40(5), 927-944
[Journal article]Authored by: Martin, G.
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Gehring, FW., Gilman, JP., & Martin, GJ. (2001). Kleinian groups with real parameters. Communications in Contemporary Mathematics. 3(2), 163-186
[Journal article]Authored by: Martin, G.
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Bonfert-Taylor, P., & Martin, G. (2001). Quasiconformal groups with small dilatation I. Proceedings of the American Mathematical Society. 129(7), 2019-2029
[Journal article]Authored by: Martin, G.
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Astala, K., Iwaniec, T., Koskela, P., & Martin, G. (2000). Mappings of B M O-bounded distortion. Mathematische Annalen. 317(4), 703-726
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1999). The hilbert-smith conjecture for quasiconformal actions. Electronic Research Announcements of the American Mathematical Society. 5(9), 66-70
[Journal article]Authored by: Martin, G.
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Gehring, FW., & Martin, GJ. (1999). The volume of hyperbolic 3-folds with P-torsion, P ≥ 6. Quarterly Journal of Mathematics. 50(197), 1-12
[Journal article]Authored by: Martin, G.
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Bargmann, D., Bonk, M., Hinkkanen, A., & Martin, GJ. (1999). Families of meromorphic functions avoiding continuous functions. Journal d'Analyse Mathematique. 79, 379-387
[Journal article]Authored by: Martin, G.
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Maclachlan, C., & Martin, GJ. (1999). 2-generator arithmetic Kleinian groups. Journal fur die Reine und Angewandte Mathematik. 511, 95-117
[Journal article]Authored by: Martin, G.
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Gehring, FW., & Martin, GJ. (1998). Precisely invariant collars and the volume of hyperbolic 3-folds. Journal of Differential Geometry. 49(3), 411-435
[Journal article]Authored by: Martin, G.
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Gehring, FW., Marshall, TH., & Martin, GJ. (1998). The spectrum of elliptic axial distances in Kleinian groups. Indiana University Mathematics Journal. 47(1), 1-10
[Journal article]Authored by: Martin, G.
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Gehring, FW., Maclachlan, C., & Martin, GJ. (1998). Two-generator arithmetic Kleinian groups II. Bulletin of the London Mathematical Society. 30(3), 258-266
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1997). Branch sets of uniformly quasiregular maps. Conformal Geometry and Dynamics. 1(3), 24-27
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1997). The distortion theorem for quasiconformal mappings, Schottky's theorem and holomorphic motions. Proceedings of the American Mathematical Society. 125(4), 1095-1103
[Journal article]Authored by: Martin, G.
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Gehring, FW., & Martin, GJ. (1997). Geodesics in hyperbolic 3-folds. Michigan Mathematical Journal. 44(2), 331-343
[Journal article]Authored by: Martin, G.
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Gehring, FW., Maclachlan, C., Martin, GJ., & Reid, AW. (1997). Arithmeticity, discreteness and volume. Transactions of the American Mathematical Society. 349(9), 3611-3643
[Journal article]Authored by: Martin, G.
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Iwaniec, T., & Martin, G. (1996). Riesz transforms and related singular integrals To the memory of Antoni Zygmund. Journal fur die Reine und Angewandte Mathematik. 1996(473), 25-58
[Journal article]Authored by: Martin, G.
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Iwaniec, T., & Martin, G. (1996). Riesz transforms and related singular integrals. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK. 473, 25-57
[Journal article]Authored by: Martin, G.
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Hinkkanen, A., & Martin, GJ. (1996). The dynamics of semigroups of rational functions I. Proceedings of the London Mathematical Society. 73(2), 358-384
[Journal article]Authored by: Martin, G.
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Hinkkanen, A., & Martin, GJ. (1996). Julia sets of rational semigroups. Mathematische Zeitschrift. 222(2), 161-169
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1996). Triangle subgroups of Kleinian groups. Commentarii Mathematici Helvetici. 71(1), 339-361
[Journal article]Authored by: Martin, G.
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Iwaniec, T., & Martin, G. (1996). Quasiregular semigroups. Annales Academiae Scientiarum Fennicae Mathematica. 21(2), 241-254
[Journal article]Authored by: Martin, G.
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Gehring, FW., & Martin, GJ. (1996). On the Margulis constant for Kleinian groups, I. Annales Academiae Scientiarum Fennicae Mathematica. 21(2), 439-462
[Journal article]Authored by: Martin, G.
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HINKKANEN, A., & MARTIN, GJ. (1994). ABELIAN NONDISCRETE CONVERGENCE GROUPS IN THE PLANE. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA. 19(2), 205-246
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1994). Complex dynamical systems. International Journal of Mathematical Education in Science and Technology. 25(6), 879-897
[Journal article]Authored by: Martin, G.
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1
Gehring, FW., & Martin, GJ. (1994). Commutators, collars and the geometry of Möbius groups. Journal d'Analyse Mathématique. 63(1), 175-219
[Journal article]Authored by: Martin, G.
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GAULD, DB., & MARTIN, GJ. (1993). ESSENTIAL SINGULARITIES OF QUASI-MEROMORPHIC MAPPINGS. MATHEMATICA SCANDINAVICA. 73(1), 36-40
[Journal article]Authored by: Martin, G.
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GEHRING, FW., & MARTIN, GJ. (1993). 6-TORSION AND HYPERBOLIC VOLUME. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 117(3), 727-735
[Journal article]Authored by: Martin, G.
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9
Conder, MDE., & Martin, GJ. (1993). Cusps, triangle groups and hyperbolic 3-folds. Journal of the Australian Mathematical Society. 55(2), 149-182
[Journal article]Authored by: Martin, G.
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Gehring, FW., & Martin, GJ. (1993). 6-Torsion and hyperbolic volume. Proceedings of the American Mathematical Society. 117(3), 727-735
[Journal article]Authored by: Martin, G.
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9
Iwaniec, T., & Martin, G. (1993). Quasiregular mappings in even dimensions. Acta Mathematica. 170(1), 29-81
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1993). On discrete isometry groups of negative curvature. Pacific Journal of Mathematics. 160(1), 109-127
[Journal article]Authored by: Martin, G.
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LEVENBERG, N., MARTIN, G., & POLETSKY, EA. (1992). ANALYTIC DISKS AND PLURIPOLAR SETS. INDIANA UNIVERSITY MATHEMATICS JOURNAL. 41(2), 515-532
[Journal article]Authored by: Martin, G.
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MARTIN, GJ., & TUKIA, P. (1992). CONVERGENCE GROUPS WITH AN INVARIANT COMPONENT PAIR. AMERICAN JOURNAL OF MATHEMATICS. 114(5), 1049-1077
[Journal article]Authored by: Martin, G.
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5
Gehring, FW., & Martin, GJ. (1992). Axial distances in discrete Möbius groups. Proceedings of the National Academy of Sciences of the United States of America. 89(6), 1999-2001
[Journal article]Authored by: Martin, G.
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IWANIEC, T., & MARTIN, G. (1991). QUASI-CONFORMAL MAPPINGS AND CAPACITY. INDIANA UNIVERSITY MATHEMATICS JOURNAL. 40(1), 101-122
[Journal article]Authored by: Martin, G.
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13
Gehring, FW., & Martin, GJ. (1991). Inequalities for Mobius transformations and discrete groups. Journal fur die Reine und Angewandte Mathematik. 1991(418), 31-76
[Journal article]Authored by: Martin, G.
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Ferrand, J., Martin, GJ., & Vuorinen, M. (1991). Lipschitz conditions in conformally invariant metrics. Journal d'Analyse Mathématique. 56(1), 187-210
[Journal article]Authored by: Martin, G.
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David, G., Martin, G., & Semmes, S. (1990). Mediatrice de deux arcs de quasicercle. Journal d'Analyse Mathematique. 55(1), 250-270
[Journal article]Authored by: Martin, G.
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MARTIN, GJ., & SKORA, RK. (1989). GROUP-ACTIONS OF THE 2-SPHERE. AMERICAN JOURNAL OF MATHEMATICS. 111(3), 387-402
[Journal article]Authored by: Martin, G.
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12
Martin, GJ. (1989). Quasiconformal and affine groups. Journal of Differential Geometry. 29(2), 427-448
[Journal article]Authored by: Martin, G.
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Gehring, W., & Martin, GJ. (1989). Iteration theory and inequalities for kleinian groups. Bulletin of the American Mathematical Society. 21(1), 57-63
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1989). Balls in hyperbolic manifolds. Journal of the London Mathematical Society. s2-40(2), 257-264
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1989). On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality. Acta Mathematica. 163(1), 253-289
[Journal article]Authored by: Martin, G.
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LEVENBERG, N., MARTIN, GJ., SHIELDS, AL., & ZDRAVKOVSKA, S. (1988). FACTORIZATIONS OF LEBESGUE MEASURE VIA CONVOLUTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 104(2), 419-430
[Journal article]Authored by: Martin, G.
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Levenberg, N., Martin, GJ., Shields, AL., & Zdravkovska, S. (1988). Factorizations of lebesgue measure via convolutions. Proceedings of the American Mathematical Society. 104(2), 419-430
[Journal article]Authored by: Martin, G.
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5
Gehring, FW., & Martin, GJ. (1987). Discrete quasiconformal groups I. Proceedings of the London Mathematical Society. s3-55(2), 331-358
[Journal article]Authored by: Martin, G.
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Martin, GJ., & Osgood, BG. (1986). The quasihyperbolic metric and associated estimates on the hyperbolic metric. Journal d'Analyse Mathématique. 47(1), 37-53
[Journal article]Authored by: Martin, G.
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MARTIN, GJ. (1985). QUASI-CONFORMAL AND BI-LIPSCHITZ HOMEOMORPHISMS, UNIFORM DOMAINS AND THE QUASIHYPERBOLIC METRIC. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 292(1), 169-191
[Journal article]Authored by: Martin, G.
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Martin, GJ. (1985). Quasiconformal and bi-lipschitz homeomorphisms, uniform domains and the quasihyperbolic metric. Transactions of the American Mathematical Society. 292(1), 169-191
[Journal article]Authored by: Martin, G.
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Book

Marshall, TH., & Martin, G. (2024). Polynomial Trace Identities in SL(2, C), Quaternion Algebras, and Two-Generator Kleinian Groups. In Handbook of Complex Analysis. (pp. 433 - 486).
[Chapter]Authored by: Martin, G.
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Flambaum, V., Martin, G., & Pavlov, B. (2020). A resonance interaction of seismogravitational modes on tectonic plates. In Operator Theory: Advances and Applications. (pp. 305 - 334).
[Chapter]Authored by: Martin, G.
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2
Gehring, FW., Martin, GJ., & Palka, BP.(2017). An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings. : American Mathematical Soc.
[Authored Book]Authored by: Martin, G.
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Martin, GJ. (2015). The geometry and arithmetic of kleinian groups. In L. Ji, P. Athanase, & S-T. Yau (Eds.) Handbook of Group Actions, Volume I. (pp. 412 - 494). Massachusetts, USA: International Press of Boston
[Chapter]Authored by: Martin, G.
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Martin, GJ. (2014). The theory of quasiconformal mappings in higher dimensions, I. In A. Papadopoulos (Ed.) Handbook of Teichmüller theory, Vol. IV. (pp. 619 - 677). : European Mathematical Society
[Chapter]Authored by: Martin, G.

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Martin, GJ. (2013). New approaches to modeling elastic media. In Y. Mastai (Ed.) Materials Science - Advanced Topics. (pp. 465 - 485). : INTECH
[Chapter]Authored by: Martin, G.
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Astala, K., Iwaniec, T., & Martin, G. (2008). Elliptic partial differential equations and quasiconformal mappings in the plane (PMS-48).
[Monograph]Authored by: Martin, G.
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245
Astala, K., Iwaniec, T., & Martin, G.(2008). Elliptic partial differential equations and quasiconformal mappings in the plane.
[Authored Book]Authored by: Martin, G.
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181
Astala, K., Iwaniec, T., Martin, G., & Onninen, J. (2008). Schottky's theorem on conformal mappings between annuli: A play of derivatives and integrals. In M. Agranovsky, D. Bshouty, L. Karp, S. Reich, D. Shoikhet, & L. Zalcman (Eds.) Complex Analysis and Dynamical Systems III Contemporary Mathematics Series. (pp. 35 - 39). United States: Amer Mathematical Society
[Chapter]Authored by: Martin, G.
Iwaniec, T., Iwaniec, JRFDPOMT., Martin, G., & Martin, POMG.(2001). Geometric Function Theory and Non-linear Analysis. : Clarendon Press
[Authored Book]Authored by: Martin, G.
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Conference

Martin, GJ. (2013, August). Lp Teichmuller Theory. Presented at 22nd Rolf Nevanlinna Conference, August 2013. Helsinki,.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, GJ. (2013, May). Solution to Siegel's Problem. Presented at Groups and geometry in the South East, May 2013. LMS network, Oxford,.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, GJ. (2013, May). The work of Kari Astala. Presented at Quasiconformal Geometry and Elliptic PDEs. UCLA.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, GJ. (2013, April). New approaches to nonlinear elasticity. Presented at Interactions between geometry analysis. Institute for Pure & Applied Mathematics, Los Angeles.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, GJ. (2012, June). Extremal problems and Teichmuller theory. Presented at International conference in Geometric and Nonlinear Partial Differential Equation. Jiaotong University Xi'an.
[Conference Oral Presentation]Authored by: Martin, G.

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Martin, GJ. (2010, August). Mappings of finite distortion and Teichmuller spaces. Presented at Geometry, Topology and Dynamics of Character Varieties http://www2.ims.nus.edu.sg/Programs/010geometry/index.php
[Conference Oral Presentation]Authored by: Martin, G.
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Martin, G. (2010, January). The governing PDE's for nonlinear materials science conformal geometry and the Hibert Smith Conjecture. Presented at International Conference on Analysis and Applications. Sultan Qaboos University, Oman.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2010, September). Quasiregular mappings, curvature and dynamics. Presented at 54th Annual Meeting of the Australian Mathematical Society. University of Queensland, Australia.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2010, August). Quasiregular mappings curvature and dynamics. Presented at International Congress of Mathematicians. Hyderabad, India.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, GJ.Quasiregular mappings, Curvature &amp; dynamics.
[Conference Oral Presentation]Authored by: Martin, G.
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Martin, G. (2010, August). Mappings of finite distortion and Teichmuller spaces. Presented at Conference on Geometry Topology and Dynamics of Character Varieties. National University of Singapore, Singapore.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2010, June). Mappings of finite distortion and Teichmüller spaces. Presented at HIM Trimester Program on Geometry and Dynamics of Tewichmuller Spaces. Bonn, Germany.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2010, June). Mappings of finite distortion and Teichmuller spaces. Presented at HIM trimester program on Geometry and Dynamics of Teichmuller Spaces Main Conference. Bonn, Germany.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2009, June). Minimisers of weighted mean distortion and models for nonlinear elasticity. Presented at European Science Foundation Conference in Partnership with European Mathematical Society and ERCOM: Harmonic Analysis Geometric Measure Theory and Quasiconformal Mappings. Bellaterra, Spain.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2008, May). Nische phenomena and minimizers of distortion functionals. Presented at Recent Advances in Geometric Function Theory. Syracuse University, United States.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2008, May). Stoilow factorisation for general linear systems in two dimensions. Presented at Quasiconformal Mappings and Analysis on Metric Spaces. University of Michigan, United States.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2007, December). Curvature and dynamics. Presented at Joint Meeting of the AMS - NZMS. Victoria University of Wellington, New Zealand.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2007, October). The mathematical life and work of Tadeusz IWANIEC. Presented at "Geometric Function Theory and Nonlinear analysis" on the occasion of the 60th birthday of Tadeusz Iwaniec. Naples, Italy.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2007, December). Conformal geometry. Presented at Fourth Pacific Rim Conference on Mathematics. City University of Hong Kong, Hong Kong.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2006, January). Quasiregluar mappings, knotted branch sets and hyperbolic groups. Presented at NZ-Japan Knot Theory Conference. University of Auckland, New Zealand.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G., Astala, K., & Iwaniec, T. (2006, June). Bi-Lipschitz homeomorphisms of the circle and non-linear Beltrami euqations. Presented at Analysis and Partial Differential Equations conference in honor of Professor Bogdan Borjarski. Bedlewo, Poland.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2006, September). Nonlinear Beltrami equations and bilipschitz mappings. Presented at ICM Satellite Conference. Naples, Italy.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, G. (2006, December). Curvature and dynamics. Presented at 8th Pacific Rim Geometry Conference. Murramarang Resort,South Durras, NSW, Australia.
[Conference Oral Presentation]Authored by: Martin, G.
Martin, GJ.On the geometry of Kleinian groups. QUASICONFORMAL MAPPINGS AND ANALYSIS. (pp. 253 - 274).
[Conference]Authored by: Martin, G.
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Teaching and Supervision

Contact Supervisor

Summary of Doctoral Supervision

Position Current Completed
Main Supervisor 2 9
Co-supervisor 2 3

Current Doctoral Supervision

Main Supervisor of:

  • Michael Florincescu - Doctor of Philosophy
    The Ahlfors-Hopf equation in the calculus of variations
  • Abdoulbaset Biabani - Doctor of Philosophy
    Character varieties, inequalities and discrete groups.

Co-supervisor of:

  • Hongwei Zhang - Doctor of Philosophy
    Novel Approaches for Unsupervised Person Re-identification
  • Guoqing Zhang - Doctor of Philosophy
    Research on Person Re-identification based on Deep Learning

Completed Doctoral Supervision

Main Supervisor of:

  • 2024 - Keyvan Salehi - Doctor of Philosophy
    The $(5, p)$-Arithmetic Hyperbolic Lattices in Three Dimensions
  • 2022 - Seyed Mohsen Hashemi - Doctor of Philosophy
    The Generic Failure of Lower-semicontinuity for the Linear Distortion Functional
  • 2019 - Cong Yao - Doctor of Philosophy
    Minimisation of Mean Exponential Distortions and Teichmuller Theory
  • 2018 - Graeme O'Brien - Doctor of Philosophy
    Random discrete groups of mobius transformations
  • 2014 - Adam Ward - Doctor of Philosophy
    On Essential Self-adjointness,Confining Potentials & the Lp-Hardy Inequality
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  • 2013 - Samuel Dillon - Doctor of Philosophy
    Resolving Decomposition By Blowing Up Points And Quasiconformal Harmonic Extensions
  • 2013 - Haydn Cooper - Doctor of Philosophy
    Discrete Groups and Computational Geometry
  • 2010 - Qingxiang Zhang - Doctor of Philosophy
    Two elliptic generator kleinian groups
  • 2010 - Maarten McKubre - Jordens - Doctor of Philosophy
    Minimising weighted mean distortion
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Co-supervisor of:

  • 2020 - Christian Bl盲sche - Doctor of Philosophy
    Dynamical effects of degree correlations in networks of type I model neurons
  • 2020 - Tong Liu - Doctor of Philosophy
    Improved K-means Clustering Algorithms
  • 2016 - Carlo Danieli - Doctor of Philosophy
    Advances in Classical and Quantum Wave Dynamics on Quasiperiodic Lattices