Professor Norman J Wildberger
Honorary Professor

Professor Norman J Wildberger

Science
School of Mathematics & Statistics

Born and raised in Canada, I now enjoy the warmer Australian life-style, but still like to visit my home country. I was educated at Adam Scott High School in Peterboro Ontario, Richmond Hill High School in Richmond Hill Ontario, University of Toronto (BSC 1979) and Yale University (PhD 1984). I taught at Stanford University (1984-1986) and the University of Toronto (1986-1989) before coming to UNSW (University of New South Wales), Sydney, in 1990. My wife Kim and I have a daughter Ali.

ACADEMIC QUALIFICATIONS

University of Toronto, Bachelor of Science Yale University, Doctor of Philosophy

RESEARCH INTERESTS

Lie groups, representation theory, hypergroups, geometry, rational trigonometry, foundations of mathematics, mathematical physics, Old Babylonian mathematics

TEACHING DUTIES

  • Many undergraduate courses in the School of Mathematics, including Calculus, Linear Algebra, Several variable calculus, History of Mathematics, Differential Geometry, Groups and Transformations, Coding and Information theory, Harmonic Analysis, Lie Groups, Representation theory, Geometry, Algebraic Topology, Classical Themes in Mathematics, and Logic and Computability.

SELECTED PUBLICATIONS

Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg Books, 2015)

Phone
9385 7098
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 4108
  • Books | 2005
    Wildberger NJ, 2005, Divine Proportions: Rational Trigonometry to Universal Geometry, Original, Wild Egg Pty. Ltd, Australia
  • Book Chapters | 2018
    Wildberger N; Mansfield D, 2018, 'Written in stone: The world's first trigonometry revealed in an ancient Babylonian tablet', in Pitici M (ed.), The Best Writing on Mathematics 2018, Princeton University Press, Princeton, pp. 179 - 184
  • Journal articles | 2020
    HO JC; Wildberger NJ, 2020, 'A CASE STUDY IN UNIVERSAL GEOMETRY: EXTENDING APOLLONIAN CIRCLES TO RELATIVISTIC GEOMETRY AND FINITE FIELDS', Siberian Electronic Mathematical Reports, vol. 17, pp. 1227 - 1257, http://dx.doi.org/10.33048/semi.2020.17.091
    Journal articles | 2020
    Choi SC; Wildberger N, 2020, 'Parabolic Triangles, Poles and Centroid Relations', KoG, pp. 3 - 11, http://dx.doi.org/10.31896/k.24.1
    Journal articles | 2020
    Beare W; Wildberger N, 2020, 'The Feuerbach Theorem and Cyclography in Universal Geometry', KoG, pp. 47 - 58, http://dx.doi.org/10.31896/k.24.5
    Journal articles | 2020
    Wildberger NJ, 2020, 'The Mutation Game, Coxeter-Dynkin Graphs, and Generalized Root Systems', Algebra Colloquium, vol. 27, pp. 55 - 78, http://dx.doi.org/10.1142/S1005386720000061
    Journal articles | 2020
    Le N; Wildberger NJ, 2020, 'The pentagrammum mysticum, twelve special conics and the twisted icosahedron', Journal for Geometry and Graphics, vol. 24, pp. 175 - 191
    Journal articles | 2018
    Wildberger NJ, 2018, 'Universal hyperbolic geometry, sydpoints and finite fields: A projective and algebraic alternative', Universe, vol. 4, pp. 3 - 3, http://dx.doi.org/10.3390/universe4010003
    Journal articles | 2018
    Choi SC; Wildberger N, 2018, 'The Universal Parabola', KoG, pp. 24 - 40, http://dx.doi.org/10.31896/k.22.4
    Journal articles | 2018
    Wildberger N, 2018, 'Rotor coordinates, vector trigonometry and quadrilaterals, with applications to the four bar linkage', Journal for Geometry and Graphics, vol. No. 2, pp. 257 - 268
    Journal articles | 2017
    Mansfield DF; Wildberger NJ, 2017, 'Plimpton 322 is Babylonian exact sexagesimal trigonometry', Historia Mathematica, vol. 44, pp. 395 - 419, http://dx.doi.org/10.1016/j.hm.2017.08.001
    Journal articles | 2017
    Wildberger N, 2017, 'Rational Trigonometry in Higher Dimensions and a Diagonal Rule for $2$-planes in Four-dimensional Space', KoG, pp. 47 - 54, http://dx.doi.org/10.31896/k.21.2
    Journal articles | 2017
    Wildberger NJ, 2017, 'Rotor coordinates and vector trigonometry', Journal for Geometry and Graphics, vol. 21, pp. 89 - 106
    Journal articles | 2016
    Le N; Wildberger NJ, 2016, 'Incenter symmetry, Euler lines, and Schiffler points', KoG, vol. 20, pp. 22 - 30, http://www.hdgg.hr/kog
    Journal articles | 2016
    Blefari S; Wildberger NJ, 2016, 'Quadrangle centroids in universal hyperbolic geometry', KoG, vol. 20, pp. 41 - 60, http://www.hdgg.hr/kog
    Journal articles | 2016
    Bloom WR; Wildberger NJ, 2016, 'Positive Definiteness on Spheres and Hyperbolic Spaces', Communications on Stochastic Analysis, vol. 10, pp. 541 - 559
    Journal articles | 2016
    Wildberger NJ; Alkhaldi A, 2016, 'The Parabola in Universal Hyperbolic Geometry II: Canonical Points and the Y-conic', Journal for Geometry and Graphics, vol. 20, pp. 1 - 11
    Journal articles | 2014
    Wildberger NJ; Nguyen L, 2014, 'Incenter Circles, Chromogeometry, and the Omega Triangle', KoG, vol. 18, pp. 5 - 18, http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=197552&lang=en
    Journal articles | 2013
    Wildberger NJ, 2013, 'Universal Hyperbolic Geometry I: Trigonometry', Geometriae Dedicata, vol. 163, pp. 215 - 274, http://dx.doi.org/10.1007/s10711-012-9746-9
    Journal articles | 2013
    Wildberger NJ; Alkhaldi A, 2013, 'The Parabola in Universal Hyperbolic Geometry I', KoG, vol. 17, pp. 14 - 42, http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=169113
    Journal articles | 2012
    Le N; Wildberger NJ, 2012, 'Universal affine triangle geometry and four-fold incenter symmetry', KoG, vol. 16, pp. 63 - 80, http://master.grad.hr/hdgg/kog_stranica/kog16/63-80.pdf
    Journal articles | 2012
    Wildberger NJ; Alkhaldi A, 2012, 'Universal Hyperbolic Geometry IV: Sydpoints and twin circumcircles', KoG, vol. 16, pp. 43 - 62, http://master.grad.hr/hdgg/kog_stranica/kog16/43-62.pdf
    Journal articles | 2011
    Wildberger NJ, 2011, 'Universal Hyperbolic Geometry III: First steps in Projective Triangle Geometry', KoG, vol. 15, pp. 25 - 49, http://www.hdgg.hr/kog
    Journal articles | 2010
    Wildberger NJ, 2010, 'Chromogeometry', Mathematical Intelligencer, vol. 32, pp. 26 - 32, http://dx.doi.org/10.1007/s00283-009-9077-3
    Journal articles | 2010
    Wildberger NJ, 2010, 'Pell's equation without irrational numbers', Journal of Integer Sequences, vol. 13, pp. 1 - 11
    Journal articles | 2010
    Wildberger NJ, 2010, 'Universal Hyperbolic Geometry II: A pictorial overview', KoG, vol. 14, pp. 1 - 23
    Journal articles | 2010
    Wildberger NJ, 2010, 'Greek geometry, rational trigonometry, and the Snellius-Pothenot surveying problem', Chamchuri Journal of Mathematics, vol. 2, pp. 1 - 14
    Journal articles | 2010
    Wildberger NJ, 2010, 'Pell's equation without irrational numbers', Journal of Integer Sequences, vol. 13, pp. Article 10.4.3
    Journal articles | 2009
    Goh S; Wildberger NJ, 2009, 'Spread polynomials, rotations and the butterfly effect', ArXiv, https://arxiv.org/abs/0911.1025
    Journal articles | 2009
    Wildberger NJ, 2009, 'Chromogeometry and Relativistic Conics', KoG, vol. 13, pp. 43 - 50
    Journal articles | 2008
    Alverson L; Donnelly R; Lewis SJ; McClard M; Pervine R; Proctor R; Wildberger NJ, 2008, 'DISTRIBUTIVE LATTICES DEFINED FOR REPRESENTATIONS OF RANK TWO SEMISIMPLE LIE ALGEBRAS', SIAM Journal on Discrete Mathematics, vol. 23, pp. 527 - 559, http://dx.doi.org/10.1137/070689887
    Journal articles | 2008
    Wildberger NJ, 2008, 'Neuberg cubics over finite fields', ArXiv, http://web.maths.unsw.edu.au/~norman/papers/Neuberg2.pdf
    Journal articles | 2008
    Wildberger NJ, 2008, 'The ancient Greeks present: Rational Trigonometry', ArXiv, http://adsabs.harvard.edu/abs/2008arXiv0806.3481W
    Journal articles | 2007
    Wildberger NJ, 2007, 'One dimensional metrical geometry', Geometriae Dedicata, vol. 128, pp. 145 - 166, http://dx.doi.org/10.1007/s10711-007-9187-z
    Journal articles | 2006
    Wildberger NJ, 2006, 'Affine and projective universal geometry', ArXiv, http://web.maths.unsw.edu.au/~norman/papers/AffineProjArXiV.pdf
    Journal articles | 2006
    Dooley AH; Wildberger NJ, 2006, 'Orbital convolution theory for semi-direct products', Journal of Lie Theory, vol. 16, pp. 743 - 776
    Journal articles | 2006
    Arnal D; Bel Baraka N; Wildberger NJ, 2006, 'Diamond representations of sl(n)', Annales Mathematiques Blaise Pascal, vol. 13, pp. 381 - 429
    Journal articles | 2005
    Wildberger NJ, 2005, 'Weyl quantization and a symbol calculus for abelian groups', Journal of the Australian Mathematical Society, vol. 78, pp. 323 - 338
    Journal articles | 2005
    Arnal D; Baraka NB; Wildberger NJ, 2005, 'Diamond representations of $\mathfrak{sl}(n)$', ArXiv, https://archive.org/details/arxiv-math0507435
    Journal articles | 2004
    Wildberger NJ, 2004, 'Foundations of finite group theory for a (future) computer', Mathematical Intelligencer, vol. 26, pp. 45 - 55, http://dx.doi.org/10.1007/BF02985653
    Journal articles | 2003
    Wildberger NJ, 2003, 'A combinatorial construction for simply-laced Lie algebras', Advances in Applied Mathematics, vol. 30, pp. 385 - 396, http://dx.doi.org/10.1016/S0196-8858(02)00541-9
    Journal articles | 2003
    Sunder VS; Wildberger NJ, 2003, 'Actions of finite hypergroups', Journal of Algebraic Combinatorics, vol. 18, pp. 135 - 151, http://dx.doi.org/10.1023/A:1025107014451
    Journal articles | 2003
    Wildberger NJ, 2003, 'Minuscule posets from neighbourly graph sequences', European Journal of Combinatorics, vol. 24, pp. 741 - 757, http://dx.doi.org/10.1016/S0195-6698(03)00056-8
    Journal articles | 2003
    Wildberger NJ, 2003, 'Combinatorial Construction of G2', Journal of Lie Theory, vol. 13, pp. 155 - 165
    Journal articles | 2002
    Wildberger NJ, 2002, 'Strong hypergroups of order three', Journal of Pure and Applied Algebra, vol. 174, pp. 95 - 115, http://dx.doi.org/10.1016/S0022-4049(02)00016-6
    Journal articles | 2002
    Srinivasan R; Sunder VS; Wildberger NJ, 2002, 'Discrete series of fusion algebras', Journal of the Australian Mathematical Society Series A - Pure Mathematics and Statistics, vol. 72, pp. 419 - 425, http://dx.doi.org/10.1017/S144678870003679X
    Journal articles | 2002
    Wildberger NJ, 2002, 'A new proof of Cavalieri's quadrature formula', American Mathematical Monthly, vol. 109, pp. 843 - 845, http://dx.doi.org/10.2307/3072373
    Journal articles | 2001
    Wildberger NJ, 2001, 'Algebraic structures associated to group actions and sums of Hermitian matrices', Textos de matematica Serie B, pp. 1 - 32
    Journal articles | 1999
    Wildberger NJ, 1999, 'Real fish, real numbers, real jobs', Mathematical Intelligencer, vol. 21, pp. 4 - 7, http://dx.doi.org/10.1007/BF03024838
    Journal articles | 1999
    Dooley AH; Wildberger NJ, 1999, 'Global character formulae for compact Lie groups', Transactions of the American Mathematical Society, vol. 351, pp. 477 - 495
    Journal articles | 1997
    Wildberger NJ, 1997, 'Duality and entropy for finite commutative hypergroups and fusion rule algebras', Journal of the London Mathematical Society - Second Series, vol. 56, pp. 275 - 291, http://dx.doi.org/10.1112/S0024610797005401
    Journal articles | 1996
    Obata N; Wildberger NJ, 1996, 'Generalized hypergroups and orthogonal polynomials', Nagoya Mathematical Journal, vol. 142, pp. 67 - 93, http://dx.doi.org/10.1017/S002776300000564X
    Journal articles | 1996
    Wildberger NJ, 1996, 'On the algebraic structure of Gaussian periods', Journal of Number Theory, vol. 57, pp. 278 - 291, http://dx.doi.org/10.1006/jnth.1996.0048
    Journal articles | 1996
    Wildberger NJ, 1996, 'Lagrange`s theorem and integrality for finite commutative hypergroups with applications to strongly regular graphs', Journal of Algebra, vol. 182, pp. 1 - 37, http://dx.doi.org/10.1006/jabr.1996.0158
    Journal articles | 1995
    Wildberger NJ, 1995, 'Finite commutative hypergroups and applications from group theory to conformal field theory', Contemporary Mathematics, vol. 183, pp. 413 - 434
    Journal articles | 1994
    Wildberger NJ, 1994, 'On the Fourier Transform of a Compact Semisimple Lie Group', Journal of the Australian Mathematical Society, vol. 56, pp. 64 - 116, http://dx.doi.org/10.1017/S1446788700034741
    Journal articles | 1994
    Wildberger NJ, 1994, 'Row-reduction and invariants of Diophantine equations', Proceedings of the Indian Academy of Sciences - Mathematical Sciences, vol. 104, pp. 549 - 555, http://dx.doi.org/10.1007/BF02867120
    Journal articles | 1993
    Wildberger NJ, 1993, 'Diagonalization in compact lie algebras and a new proof of a theorem of kostant', Proceedings of the American Mathematical Society, vol. 119, pp. 649 - 655, http://dx.doi.org/10.1090/S0002-9939-1993-1151817-6
    Journal articles | 1993
    Dooley AH; Wildberger NJ; Repka J, 1993, 'Sums of Adjoint Orbits', Linear and Multilinear Algebra, vol. 36, pp. 79 - 101, http://dx.doi.org/10.1080/03081089308818278
    Journal articles | 1993
    WILDBERGER NJ, 1993, 'DIAGONALIZATION IN COMPACT LIE-ALGEBRAS AND A NEW PROOF OF A THEOREM OF KOSTANT', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 119, pp. 649 - 655, http://dx.doi.org/10.2307/2159953
    Journal articles | 1993
    Dooley AH; Wildberger NJ, 1993, 'Harmonic analysis and the global exponential map for compact Lie groups', Functional Analysis and Its Applications, vol. 27, pp. 21 - 27, http://dx.doi.org/10.1007/BF01768664
    Journal articles | 1993
    Wildberger NJ, 1993, 'A deformation of the *-product of Gutt on a reductive Lie algebra', Journal of Geometry and Physics, vol. 12, pp. 217 - 222, http://dx.doi.org/10.1016/0393-0440(93)90035-D
    Journal articles | 1992
    Wildberger NJ, 1992, 'The moment map of a lie group representation', Transactions of the American Mathematical Society, vol. 330, pp. 257 - 268, http://dx.doi.org/10.1090/S0002-9947-1992-1028765-9
    Journal articles | 1992
    Wildberger NJ, 1992, 'The moment map of a lie group representation', Transactions of the American Mathematical Society, vol. 330, pp. 257 - 268, http://dx.doi.org/10.1090/S0002-9947-1992-1040046-6
    Journal articles | 1990
    Repka J; Wildberger N, 1990, 'Invariant measure on sums of symmetric 3*3 matrices with specified eigenvalues', Journal of Physics A: General Physics, vol. 23, pp. 5717 - 5724, http://dx.doi.org/10.1088/0305-4470/23/24/013
    Journal articles | 1990
    WILDBERGER NJ, 1990, 'ON A RELATIONSHIP BETWEEN ADJOINT ORBITS AND CONJUGACY CLASSES OF A LIE GROUP', CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, vol. 33, pp. 297 - 304, http://dx.doi.org/10.4153/CMB-1990-048-4
    Journal articles | 1989
    Wildberger NJ, 1989, 'Convexity and unitary representations of nilpotent Lie groups', Inventiones Mathematicae, vol. 98, pp. 281 - 292, http://dx.doi.org/10.1007/BF01388854
  • Preprints | 2006
    Wildberger NJ, 2006, Affine and projective universal geometry
    Conference Papers | 1995
    Sunder VS; Wildberger NJ, 1995, 'Actions of finite hypergroups and examples', in Ross KA; Anderson JM; Litvinov GL; Singh AI; Sunder VS; Wildberger NJ (eds.), HARMONIC ANALYSIS AND HYPERGROUPS, BIRKHAUSER BOSTON, UNIV DELHI, DELHI, INDIA, pp. 145 - 163, presented at International Conference on Harmonic Analysis, UNIV DELHI, DELHI, INDIA, 18 December 1995 - 22 December 1995, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000073104300010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1995
    Wildberger NJ, 1995, 'Characters, Bi-modules and representations in Lie group harmonic analysis', in Ross KA; Anderson JM; Litvinov GL; Singh AI; Sunder VS; Wildberger NJ (eds.), HARMONIC ANALYSIS AND HYPERGROUPS, BIRKHAUSER BOSTON, UNIV DELHI, DELHI, INDIA, pp. 227 - 242, presented at International Conference on Harmonic Analysis, UNIV DELHI, DELHI, INDIA, 18 December 1995 - 22 December 1995, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000073104300014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1994
    Wildberger NJ, 1994, 'Hypergroups, symmetric spaces, and wrapping maps', in Probability Measures on Groups and Related Structures, Probability Measures on Groups and Related Structures, Oberwolfach Germany, presented at Probability Measures on Groups and Related Structures, Oberwolfach Germany, 23 October 1994 - 29 October 1994