Professor Norman Wildberger

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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

E-mail

n.wildberger@unsw.edu.au

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 | 2022

Ho JC; Wildberger NJ, 2022, 'A Physical Archimedean Approach to Affine Geometry and the Remarkable 13 (Mixed) Configuration', Journal for Geometry and Graphics, 26, pp. 65 - 80

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

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

HO JC; Wildberger NJ, 2020, 'A CASE STUDY IN UNIVERSAL GEOMETRY: EXTENDING APOLLONIAN CIRCLES TO RELATIVISTIC GEOMETRY AND FINITE FIELDS', Siberian Electronic Mathematical Reports, 17, pp. 1227 - 1257, http://dx.doi.org/10.33048/semi.2020.17.091

Journal articles | 2020

Le N; Wildberger NJ, 2020, 'The pentagrammum mysticum, twelve special conics and the twisted icosahedron', Journal for Geometry and Graphics, 24, pp. 175 - 191

Journal articles | 2020

Wildberger NJ, 2020, 'The Mutation Game, Coxeter-Dynkin Graphs, and Generalized Root Systems', Algebra Colloquium, 27, pp. 55 - 78, http://dx.doi.org/10.1142/S1005386720000061

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, No. 2, pp. 257 - 268

Journal articles | 2018

Wildberger NJ, 2018, 'Universal hyperbolic geometry, sydpoints and finite fields: A projective and algebraic alternative', Universe, 4, pp. 3, http://dx.doi.org/10.3390/universe4010003

Journal articles | 2017

Mansfield DF; Wildberger NJ, 2017, 'Plimpton 322 is Babylonian exact sexagesimal trigonometry', Historia Mathematica, 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, 21, pp. 89 - 106

Journal articles | 2016

Blefari S; Wildberger NJ, 2016, 'Quadrangle centroids in universal hyperbolic geometry', KoG, 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, 10, pp. 541 - 559

Journal articles | 2016

Le N; Wildberger NJ, 2016, 'Incenter symmetry, Euler lines, and Schiffler points', KoG, 20, pp. 22 - 30, http://www.hdgg.hr/kog

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, 20, pp. 1 - 11

Journal articles | 2014

Wildberger NJ; Nguyen L, 2014, 'Incenter Circles, Chromogeometry, and the Omega Triangle', KoG, 18, pp. 5 - 18, http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=197552&lang=en

Journal articles | 2013

Wildberger NJ; Alkhaldi A, 2013, 'The Parabola in Universal Hyperbolic Geometry I', KoG, 17, pp. 14 - 42, http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=169113

Journal articles | 2013

Wildberger NJ, 2013, 'Universal Hyperbolic Geometry I: Trigonometry', Geometriae Dedicata, 163, pp. 215 - 274, http://dx.doi.org/10.1007/s10711-012-9746-9

Journal articles | 2012

Le N; Wildberger NJ, 2012, 'Universal affine triangle geometry and four-fold incenter symmetry', KoG, 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, 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, 15, pp. 25 - 49, http://www.hdgg.hr/kog

Journal articles | 2010

Wildberger NJ, 2010, 'Chromogeometry', Mathematical Intelligencer, 32, pp. 26 - 32, http://dx.doi.org/10.1007/s00283-009-9077-3

Journal articles | 2010

Wildberger NJ, 2010, 'Greek geometry, rational trigonometry, and the Snellius-Pothenot surveying problem', Chamchuri Journal of Mathematics, 2, pp. 1 - 14

Journal articles | 2010

Wildberger NJ, 2010, 'Pell's equation without irrational numbers', Journal of Integer Sequences, 13, pp. 1 - 11

Journal articles | 2010

Wildberger NJ, 2010, 'Pell's equation without irrational numbers', Journal of Integer Sequences, 13, pp. Article 10.4.3

Journal articles | 2010

Wildberger NJ, 2010, 'Universal Hyperbolic Geometry II: A pictorial overview', KoG, 14, pp. 1 - 23

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, 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, 23, pp. 527 - 559

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, 128, pp. 145 - 166

Journal articles | 2006

Arnal D; Bel Baraka N; Wildberger NJ, 2006, 'Diamond representations of sl(n)', Annales Mathematiques Blaise Pascal, 13, pp. 381 - 429

Journal articles | 2006

Dooley AH; Wildberger NJ, 2006, 'Orbital convolution theory for semi-direct products', Journal of Lie Theory, 16, pp. 743 - 776

Journal articles | 2006

Wildberger NJ, 2006, 'Affine and projective universal geometry', ArXiv, http://web.maths.unsw.edu.au/~norman/papers/AffineProjArXiV.pdf

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 | 2005

Wildberger NJ, 2005, 'Weyl quantization and a symbol calculus for abelian groups', Journal of the Australian Mathematical Society, 78, pp. 323 - 338

Journal articles | 2004

Wildberger NJ, 2004, 'Foundations of finite group theory for a (future) computer', Mathematical Intelligencer, 26, pp. 45 - 55

Journal articles | 2003

Sunder VS; Wildberger NJ, 2003, 'Actions of finite hypergroups', Journal of Algebraic Combinatorics, 18, pp. 135 - 151

Journal articles | 2003

Wildberger NJ, 2003, 'A combinatorial construction for simply-laced Lie algebras', Advances in Applied Mathematics, 30, pp. 385 - 396

Journal articles | 2003

Wildberger NJ, 2003, 'Combinatorial Construction of G2', Journal of Lie Theory, 13, pp. 155 - 165

Journal articles | 2003

Wildberger NJ, 2003, 'Minuscule posets from neighbourly graph sequences', European Journal of Combinatorics, 24, pp. 741 - 757

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, 72, pp. 419 - 425

Journal articles | 2002

Wildberger NJ, 2002, 'A new proof of Cavalieri's quadrature formula', American Mathematical Monthly, 109, pp. 843 - 845, http://dx.doi.org/10.2307/3072373

Journal articles | 2002

Wildberger NJ, 2002, 'Strong hypergroups of order three', Journal of Pure and Applied Algebra, 174, pp. 95 - 115

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

Dooley AH; Wildberger NJ, 1999, 'Global character formulae for compact Lie groups', Transactions of the American Mathematical Society, pp. 477 - 495

Journal articles | 1999

Wildberger NJ, 1999, 'Real fish, real numbers, real jobs', Mathematical Intelligencer, 21, pp. 4 - 7, http://dx.doi.org/10.1007/BF03024838

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, pp. 275 - 291

Journal articles | 1996

Obata N; Wildberger NJ, 1996, 'Generalized hypergroups and orthogonal polynomials', Nagoya Mathematical Journal, 142, pp. 67 - 93, http://dx.doi.org/10.1017/S002776300000564X

Journal articles | 1996

Wildberger NJ, 1996, 'Lagrange`s theorem and integrality for finite commutative hypergroups with applications to strongly regular graphs', Journal of Algebra, 182, pp. 1 - 37, http://dx.doi.org/10.1006/jabr.1996.0158

Journal articles | 1996

Wildberger NJ, 1996, 'On the algebraic structure of Gaussian periods', Journal of Number Theory, 57, pp. 278 - 291, http://dx.doi.org/10.1006/jnth.1996.0048

Journal articles | 1995

Wildberger NJ, 1995, 'Finite commutative hypergroups and applications from group theory to conformal field theory', Contemporary Mathematics, 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, 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, 104, pp. 549 - 555, http://dx.doi.org/10.1007/BF02867120

Journal articles | 1993

Dooley AH; Wildberger NJ; Repka J, 1993, 'Sums of Adjoint Orbits', Linear and Multilinear Algebra, 36, pp. 79 - 101, http://dx.doi.org/10.1080/03081089308818278

Journal articles | 1993

Dooley AH; Wildberger NJ, 1993, 'Harmonic analysis and the global exponential map for compact Lie groups', Functional Analysis and Its Applications, 27, pp. 21 - 27, http://dx.doi.org/10.1007/BF01768664

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, 119, pp. 649 - 655, http://dx.doi.org/10.2307/2159953

Journal articles | 1993

Wildberger NJ, 1993, 'A deformation of the *-product of Gutt on a reductive Lie algebra', Journal of Geometry and Physics, 12, pp. 217 - 222, http://dx.doi.org/10.1016/0393-0440(93)90035-D

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, 119, pp. 649 - 655, http://dx.doi.org/10.1090/S0002-9939-1993-1151817-6

Journal articles | 1992

Wildberger NJ, 1992, 'The moment map of a lie group representation', Transactions of the American Mathematical Society, 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, 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, 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, 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, 98, pp. 281 - 292, http://dx.doi.org/10.1007/BF01388854
Preprints | 2006

Wildberger NJ, 2006, Affine and projective universal geometry, , http://dx.doi.org/10.48550/arxiv.math/0612499

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, INDIA, UNIV DELHI, DELHI, pp. 145 - 163, presented at International Conference on Harmonic Analysis, INDIA, UNIV DELHI, DELHI, 18 December 1995 - 22 December 1995, https://www.webofscience.com/api/gateway?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, INDIA, UNIV DELHI, DELHI, pp. 227 - 242, presented at International Conference on Harmonic Analysis, INDIA, UNIV DELHI, DELHI, 18 December 1995 - 22 December 1995, https://www.webofscience.com/api/gateway?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

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