Brief CV of Kevin A. Broughan

 

Tertiary Education Record

BSc      University of Auckland 1967 

     MSc     University of Auckland 1968 (First Class Honours)

     MA      Columbia University 1970

     MPhil Columbia University 1975

     PhD     Columbia University 1975

 

Employment History

            Senior Science and Mathematics Teacher, St Paul’s College, Auckland, 1967,

Junior Lecturer, University of Auckland,  1968

Teaching Assistant, Columbia University,  1969-70

Lecturer in Mathematics, University of Waikato, 1971-74,

Senior Lecturer:                                   1975-88,

Associate Professor:                1989-

Chairperson of Mathematics, University of Waikato: 1996-2001

 

Distinctions:

Dux of St. Bernard's College, 1960, 1961

Credit Pass, NZ University Scholarship Examination, 1960

NZ University National Scholarship, 1961

Applied Mathematics Prize, University of Auckland, 1965

Senior Scholarship in Mathematics and Physics, University of Auckland, 1966

Sir George Grey Scholarship, University of Auckland, 1966

Fulbright Award for study in the United States, 1968

UGC Postgraduate Scholar in Science, 1968

Faculty Fellowship, Columbia University, 1968

Columbia Ph.D. Qualifying Examination passed with Distinction, 1969

Faculty Fellowship, Columbia University, 1974-75

Senior Visiting Fellow, Cambridge University, DAMPT, 1980

Consultant to the research project on the Representation and

    Manipulation of Mathematical Knowledge, University of California

    at Berkeley, Center for Pure and Applied Mathematics 1983-84

New Zealand Computer Software Award for Senac 1991

Steering Committee for High Performance Computing - Asia conference

    series 1994-98

Programme Committee for International Conference on Symbolic and

    Algebraic Computation 1995

Visiting Professor, Department of Mathematics, Columbia University 1999,2002

Fellow of the New Zealand Mathematical Society, elected 2001

Claude-McCarthy Fellowship 1994, 2004.

Invitation to chair a session on number theory at ICM2006, Madrid.

Invited participation in the American Institute of Mathematics workshop on the computational aspects of L-functions and modular forms, 2007.

            University of Waikato Fulbright Adviser 2007-.

Joint organizer of a special session on Number Theory, joint NZ Australian Mathematics Convention, Christchurch, 2008.

 

  Memberships of Scholarly and Professional Societies:

American Mathematical Society (AMS),

New Zealand  Mathematical Society (NZMS), designation FNZMS

Institute for Professional Engineers of New Zealand (IPENZ) designation M.IPENZ,

 

Research Publications since 2000

 

Chapters in Books Authored

[1] R. E. D. Ferdinands, K. A. Broughan and H. Round, A time variant forward solution model of the bowling arm in cricket, Chapter in “Biomechanics Research in the New Millennium”, Routledge, 2002.

[2] K. A. Broughan appendix and associated software GL(n)pack in “Automorphic Forms and L-functions for the group GL(n,R)” by D. Goldfeld, Cambridge University Press, 2006.

 

Journal Articles published in refereed journals

[1] K. A. Broughan and Nan Zhu, “An integer programming problem with a linear programming solution”, Amer. Math. Monthly, 107, (2000), 444-446.

[2] K. A. Broughan, “The GCD-sum function”, Journal of Integer Sequences, 4, (2001), Article 01.2.2, (p1-19).

[3] K. A. Broughan, “Restricted Divisor Sums”, Acta Arithmetica, 101 (2002) p105-114.

[4] K. A. Broughan, “Vanishing of the integral of the Hurwitz Zeta function”, Bulletin of the Australian Mathematical Society,  65 (2002) p121-127.

[5] K. A. Broughan, “Asymptotic order of the square free part of n!”, Integers: Electronic Journal of Combinatorial Number Theory 2, A10, 2002, p1-6 .

[6] K. A. Broughan, “Adic topologies on the rational integers”, Canadian Journal of Mathematics, 55 (4) (2003) p711-723.

[7] K. A. Broughan and A. R. Barnett, “The homomorphic flow of the Riemann zeta function”, Math. Comp. 73 (2004), 987-1004.

[8] K. A. Broughan, “Holomorphic flows on simply connected subsets have no limit cycles”, Meccanica, 38 (2003), 699-709.

[9] K. A. Broughan, “Relations between the conductor and integer k’th root functions”, International Journal of Pure and Applied Mathematics, 5 (2003) p253-275).

[10] K. A. Broughan, “The structure of sectors of zeros of entire flows”, Topology Proceedings, 27 (2003), p379-394.

[11] K. A. Broughan, “Characterizing the sum of two cubes”, Journal of Integer Sequences, 6, (2003) Article 03.4.6, p1-7.

[12] K. A. Broughan, “Holomorphic flow of the Riemann Xi function”, Nonlinearity, 18, (2005), p1269-1294.

[13] K. A. Broughan and R. J. Casey, “Harmonic sets and the harmonic prime number theorem”, Bulletin of the Australian Mathematical Society , 71, (2005), p127-137.

[14]  V. A. Krysko, J. Awrejcewicz, A. N. Kutsemako, K. Broughan, “Interaction between flexible shells (plates) and a moving lumped body”, Communications in Nonlinear Science and Numerical Simulation, 11 (2006), p13-43.

[15] K. A. Broughan and A. R. Barnett, “Linear law for the logarithms of the Riemann periods at simple critical zeros”, Mathematics of Computation, 75 (2006), p891-902.

[16] K. A. Broughan, Relaxations of the ABC conjecture using integer k’th roots, NZ Journal of Mathematics, 35 (2006), 121-136.

[17] K. A. Broughan and A. Ross Barnett, “Corrigendum to the holomorphic flow of the zeta function”, 76 (2007), p2249-2250.

[18] K. A. Broughan, “Corrigenda for holomorphic flows on simply connected regions have no limit cycles”, Meccanica, 42, (2007), p213.

[19] K. A. Broughan, “The average order of the Dirichlet series of the gcd-sum function”, Journal of Integer Sequences, (2007) Article 07.4.2 , p1-6.

[20] K. A. Broughan, “Computing Casimir operators for the generalized upper half plane”, International Journal of Pure and Applied Mathematics, 41 (2007),  p549-560.

[21] K. A. Broughan and Qizhi Zhou, “Odd multiperfect numbers of abundancy 4”, Journal of Number Theory, 128 (2008), p1568-1575.

[22] K. A. Broughan, “Evaluating Jacquet’s GL(n) Whittaker function”, Mathematics of Computation, 78 (2009), p1061-1072.

[23] K. A. Broughan and A. Ross Barnett, “On primes with prime subscripts”, J. of Integer Sequences, 12 (2009) Article 09.2.3, p1-12.

 

Journal Articles accepted for publication in refereed journals

 [24] K. A. Broughan, “Extension of the Riemann xi-functions logarithmic derivative positivity region to near the critical strip” Canadian Mathematical Bulletin, accepted 2006.

 [25] K. Byard and K. A. Broughan,  “Twelfth power residue difference sets”,  Bull. Aust. Math. Soc, accepted 2008.

 [26] Kevin A. Broughan, “An algorithm for the explicit evaluation of GL(n) Kloosterman sums”, Communications in Computer Algebra, accepted 2009.

[27] Kevin A. Broughan and A. Ross Barnett, “On the number of missing values of n! modulo p”, Journal of the Ramanujan Mathematical Society, accepted 2009.

 

Journal articles submitted for publication:

Gram lines and the average of the real part of the Riemann zeta function (with Ross Barnett)

A note on Lehmer’s Euler Phi function conjecture (with Jethro van Ekeren)

On flat primes and thin primes (with Zhou Qizhi)

Some Divisibility Properties of Binomial Coefficients and Wolstenholme's conjecture (with Florian Luca and Igor Shparlinski)

On the Furstenberg closure of a class of binary recurrences (with Florian Luca)

 

Conference Proceedings-Full written papers

[28] R. E. D. Ferdinands, K. A. Broughan, and H. Round, “Cricket Bowling: a two segment Lagrangian model”, Proceedings of the 5th Australian conference on Mathematics and Computers in Sport, 5M&CS, Sydney, 2000, p197-207.

[29] R. E. D. Ferdinands, K. A. Broughan, and H. Round, “Cricket Bowling: a two segment Lagrangian model”, Proceedings of the XVIII International Symposium on Biomechanics in Sports ISBS 2000, Hong Kong, 2000, p517-520.

[30] R. E. D. Ferdinands, K. A. Broughan, Howell Round, and Robert N. Marshall, “A fifteen-segment 3D rigid body model of bowling in cricket”, Proceedings of the international conference on Computer Simulation in Biomechanics, Hongkong, 2001, p99-104.

[31] K. A. Broughan, “Holomorphic Flows have no limit cycles”, Proceedings of the 6th Conference on Dynamical Systems-Theory and Applications”, Poland, 2001, p209-222.

[32] R. E. D. Ferdinands, R. N. Marshall, H. Round and K. A. Broughan,, “Bowling arm and trunk mechanics of fast bowlers in cricket”, Proceedings of the 4th Australasian Biomechanics Conference, T. M. Bach, D Orr, R. Baker and W. A. Sparrow eds., Melbourne, 2002, p176-177.

 

 

Published Abstracts of Presented Papers

[29] K. A. Broughan, “The ABC Conjecture”, NZ Mathematics Colloquium, University of Waikato, 2000, collected abstracts.

[30] K. A. Broughan, “Restricted Divisor Sums” Grand Challenges Conference of the AMS, UCLA, Abstracts of the 956th Meeting of the AMS, p34, 2000.

[31] R. E. D. Ferdinands, K. A. Broughan, H. Round, R. N. Marshall, “A fifteen-segment 3D rigid body model of bowling in cricket”, Book of abstracts of the International Society of Biomechanics XVIIIth Congress, Switzerland, 2001, p236.

[32] K. A. Broughan, “ The topological search for long arithmetic progressions”, Devonport Topology Fest, Auckland, 2002, collected abstracts.

[33] K. A. Broughan and J. C. Turner, “The closure of the Fibonacci Numbers”,  The Tenth International Fibonacci Conference, Flagstaff, 2002, collected abstracts.

[34] K. A. Broughan, “The topological structure of holomorphic flows in the neighbourhood of a centre”, 17th Summer  Conference on Topology, University of Auckland, 2002, collected abstracts (Atlas).

[35] K. A. Broughan, “Any non-commutative hyperbolic group of transformations of the upper half plane acts discontinuously”, Devonport Topology Fest, Auckland, 2003, collected abstracts.

[36] K. A. Broughan, “Linear law for the logarithms of the Riemann zeta function periods”, NZ Mathematics Colloquium, University of Otago, 2004, collected abstracts.

[37] K. A. Broughan, “Colloquium Postscript: Universal Polish spaces and rendezvous numbers”, Devonport Topology Fest, Auckland, 2005, collected abstracts.

[38] K. A. Broughan, “Zeta zeros and holomorphic flows” International Congress of Mathematicians, Madrid, 2006.

[39] K. A. Broughan, “Gram lines provide deep insight into the nature of the Riemann zeta function”, NZ Mathematics Colloquium, University of Waikato, 2006.

[40] K. A. Broughan, “Vassiliev invariants for proper and singular knots”, Devonport Topology Fest, Auckland, 2007, collected abstracts.

[41] K. A. Broughan,  “Vanishing of the integral of the Hurwitz zeta function”, Joint NZMS AMS Conference, Wellington, 2007, collected abstracts.

[42] K. A. Broughan, “On a theorem in topological number theory describing the closure of the Fibonacci numbers”, Devonport topology Fest, Auckland, 2008, collected abstracts.

[43] K. A. Broughan and A. R. Barnett, “On the missing values of n! mod p”, Joint Australian NZ Mathematics Convention, Christchurch 2008, collected abstracts.

[44] K. A. Broughan, “Gram lines and the average of the real part of the Riemann zeta function”, AMS Meeting Urbana-Champaign, 2009.

[45] K A Broughan, “Flat primes and thin primes”,  AMS Meeting Urbana-Champaign, 2009.

[46] K A Broughan, “Tracking the Riemann zeta function with holomorphic flows”, UNAM Institute for Mathematics, Mexico and Rutgers University Number Theory Seminar, 2009.

[47] K. A. Broughan, “Holomorphic flows and the Riemann zeta function”, CUNY Graduate Center Number Theory Seminar, New York,  2009.

 

 

Contracts:

            Deed of Assignment for the Naglink software system, Development Finance

                 Corporation and University of Waikato, 1984-87

  Naglink Agreement for the distribution of the Naglink software system,

    Numerical Algorithms Group and Development Finance Corporation, 1986

  Developer Software Agreement for the use of Franz Lisp and Allegro CL

  in distributed versions of SENAC, with Franz Inc (Berkeley), 1989

  Software Distribution Agreement for the distribution of SENAC in UK/Europe

  with the University of London, 1990

  Software Distribution Agreement for the distribution of SENAC in North

  America, with Mitchell and Gauthier Associates (Concord), 1990

  Royalty sharing agreement for software and services with the Numerical

  Algorithms Group (Oxford), 1990.

  Agreement with Numerical Recipes authors for the right to translate into

  Lisp and use Numerical Recipes code in Senac, 1992.

  Water Management Software research contract with ECNZ, 1992-1994.

       Timetable Study for the University of Waikato, 1998.

 

Special activities:

Establishment of the NZ Mathematical Society, Foundation of the School of Computing and Mathematical Sciences at the University of Waikato,  Academic staff representative on the University of Waikato Council (5 years), Member University Finance Committee (4 years), Member University Academic Board (10 years), Branch Chair of AUS  (2 years) and National VP of AUS (1 year),  establishment  of the Bachelor of Engineering degree at the University of Waikato, Chair of the Department of Mathematics (6 years).

 

Kevin A. Broughan

17th April 2009