Richard Brent  Some Talks and Lectures
64th Annual Meeting of the Australian Mathematical Society,
Armidale, 8  11 December 2020
8th Number Theory Downunder Conference, Melbourne,
6  8 October 2020

The mean square error in the prime number theorem does
not have a limit
(joint work with Dave Platt and Tim Trudgian),
presented via Zoom at the
Eighth Number Theory Down Under Conference,
University of Melbourne, 7 Oct. 2020.
Overhead transparencies (beamer format):
[pdf]
Guest Lecture in MATH1510, University of Newcastle, NSW,
16 October 2019

Pitfalls in computation
presented in
MATH1510 at the
University of Newcastle, NSW, 16 Oct. 2019.
Overhead transparencies (beamer format):
[pdf]
7th Number Theory Downunder Conference, UNSW, Sydney,
31 September  3 October 2019

The multiplication table problem revisited
(joint work with Carl Pomerance, David Purdum and
Jonathan Webster),
presented at the
Seventh Number Theory Down Under Conference,
UNSW, Sydney, 2 Oct. 2019.
Overhead transparencies (beamer format):
[pdf]
AMSI/AustMS Workshop on Mathematical Thinking, Newcastle, 14  16 November 2018
6th Number Theory Downunder Conference, Canberra, 24  27 September 2018

Asymptotic expansions and conjectures related to the exponential integral
(joint work with Larry Glasser and Tony Guttmann),
presented at the
Sixth Number Theory Down Under Conference,
UNSW, Canberra, 26 Sept. 2018.
Overhead transparencies (beamer format):
[pdf]
CARMA Seminar, Newcastle, 29 May 2018

Algorithms for the Multiplication Table Problem
(joint work with Carl Pomerance and Jonathan Webster),
presented as part of the
CARMA
Special Semester in Computation and Visualisation,
Newcastle, NSW, 29 May 2018.
Overhead transparencies (beamer format):
[pdf]
Pi Day talk, Newcastle, 14 March 2018

Jonathan Borwein, Pi and the AGM
presented in memory of Jonathan Borwein (19512016)
and in celebration of "Pi Day",
Newcastle, NSW, 14 March 2018.
Overhead transparencies (beamer format):
[pdf]
5th Number Theory Downunder Conference, Bendigo, 29 September  2 October 2017
Jon Borwein Commemorative Conference (JBCC), Newcastle, NSW,
2529 September 2017
40th ACCMCC Conference, Newcastle, NSW,
1216 December 2016
Number Theory Seminar, University of NSW, 16 November 2016
4th Number Theory Downunder Conference, Newcastle, 2326 September 2016
Probabilistic and Extremal Combinatorics Downunder,
Melbourne, 1317 June 2016

Probabilistic lower bounds on maximal determinants of binary matrices
(joint work with Judyanne Osborn and Warren Smith),
presented by Judyanne Osborn and Richard Brent at
a workshop on
Probabilistic and Extremal Combinatorics Downunder,
Monash University, Melbourne, 1317 June 2016.
Overhead transparencies (beamer format):
[pdf]
Capital Number Theory, Canberra, 89 April 2016

The great trinomial hunt: an update
(joint work with Paul Zimmermann),
presented at
Capital Number Theory,
Canberra, 9 April 2016.
Overhead transparencies (beamer format):
[pdf]
CARMA Seminar, Newcastle, 27 October 2015

Some identities involving products of Gamma functions:
a case study in experimental mathematics
(joint work with Christian Krattenthaler and Ole Warnaar),
presented at a
CARMA seminar,
Newcastle, NSW, 27 October 2015.
Overhead transparencies (beamer format):
[pdf]
Shorter version:
Discrete analogues of MacdonaldMehta integrals
presented at the
Guttmann 2015  70 and Counting conference,
Newcastle, 7 December 2015.
[pdf]
Workshop on Mathematics and Computation, Newcastle, 1921 June 2015

Asymptotics of some functions arising in number theory and
analysis of algorithms
via computation and Mellin transforms
(presented at a
Workshop on Mathematics and Computation,
Newcastle, NSW, 20 June 2015).
Overhead transparencies (beamer format):
[pdf]
Gene Golub Day Memorial Workshop, Hong Kong Baptist University,
7 February 2015

Lower bounds for the Hadamard maximal determinant problem
(joint work with Judyanne Osborn and Warren Smith).
Overhead transparencies (beamer format):
[pdf]
Preprint:
arXiv:1501.06235v3
Programme and photos:
click here.
58th Annual Meeting of the Australian Mathematical Society,
Melbourne, 8 December 2014

Asymptotics of a Mahler function
(joint work with Michael Coons and Wadim Zudilin).
Overhead transparencies (beamer format):
[pdf]
Preprint:
arXiv:1412.7906v2
2nd Number Theory Down Under Conference,
Newcastle, 2425 October 2014

Twin primes (seem to be) more random than primes
(presented at the
Second Number Theory Down Under Conference,
Newcastle, NSW, 25 October 2014).
Overhead transparencies (beamer format):
[pdf]
Remark (25 May 2020): Slide 15 has been corrected.
2014 Moyal Lecture, Macquarie University, 15 October 2014

Needles, haystacks and optimal designs
(2014
Moyal Lecture, Macquarie University, 15 October 2014).
Overhead transparencies (beamer format):
[pdf]
Abstract:
[html]
57th Annual Meeting of the Australian Mathematical Society,
Sydney, 1 October 2013

Improved lower bounds on the Hadamard maxdet problem, Part I
(joint work with and presented by Judyanne Osborn).
Overhead transparencies (beamer format):
[pdf]
Preprint:
arXiv:1309.2795v2

Improved lower bounds on the Hadamard maxdet problem, Part II
(joint work with Judyanne Osborn and Warren Smith).
Overhead transparencies (beamer format):
[pdf]
Preprint (March 2014):
arXiv:1402.6817v2
University of Newcastle, first semester 2013

Lectures on the Probabilistic Method
A series of lectures on the probabilistic method,
with applications to the Hadamard maximal determinant problem.
Further details are here.
36th ACCMCC Conference, University of NSW, 1014 December 2012

Lower bounds on maximal determinants via the probabilistic method
(joint work with Warren Smith and Judyanne Osborn).
We use the probabilistic method to give improved lower bounds on the
maximal determinant of n times n {+1}
matrices.
Overhead transparencies (beamer format):
[pdf]
Preliminary version
presented at CARMA, University of Newcastle, 4 December 2012.
Preprint:
arXiv:1211.3248v2

Bounds on minors of binary matrices
(joint work with and presented by Judyanne Osborn).
Overhead transparencies (beamer format):
[pdf]
Preprint:
arXiv:1208.3330v3
56th Annual Meeting of the Australian Mathematical Society,
Ballarat, 2627 September 2012

The multiplication table, and random factored integers
(joint work with Carl Pomerance).
Overhead transparencies (beamer format):
[pdf]
Longer version presented at
HKBU, 6 February 2015:
[pdf]

Lower bounds on maximal determinants
(joint work with Judyanne Osborn).
Overhead transparencies (beamer format):
[pdf]
Paper:
arXiv:1208.1805v3
ANU, 1 August 2012

Factoring integers  an introduction
(an introductory talk to given to year 11/12 students).
Overhead transparencies (beamer format):
[pdf]
OneDay Seminar on Inverse Problems, April 2012

Inverse problems, cryptography and security
(presented at the
Second OneDay Seminar on Inverse Problems,
ANU, 13 April 2012).
This introductory talk describes some problems
that are useful in cryptography or other aspects of computer security, and
their associated inverse problems.
Overhead transparencies (beamer format):
[pdf]
Conference and Workshop in Memory of Alf van der Poorten, March 2012
Hadamard Workshop in Honour of Kathy Horadam, RMIT, Melbourne,
28 November 2011

Finding many solutions of the Hadamard maximal determinant
problem given the maximal Gram matrices
(presented at the International Workshop on
Hadamard Matrices and their Applications
in Honour of Kathy Horadam's sixtieth birthday,
RMIT University, Melbourne,
2830 November, 2011).
We describe how randomised decomposition and switching
can be used to find many solutions of the Hadamard maximal
determinant problem for certain orders.
Overhead transparencies (beamer format):
[pdf]
A related paper (appeared in
Australasian J. of Combinatorics) is here.
Workshop in Honour of Jon Borwein, Simon Fraser University, Canada,
1620 May 2011

Computing Bernoulli and Tangent numbers
(presented via videolink from Newcastle for the
Computational and Analytical Mathematics Conference
in Honour of Jonathan Borwein's sixtieth birthday,
1620 May, 2011).
We consider some algorithms for computing Bernoulli,
Secant and Tangent numbers, giving both asymptotically
fast algorithms and convenient algorithms based on
threeterm recurrences.
Video of the
talk.
Overhead transparencies (beamer format):
[pdf]
A related paper (appeared in the conference proceedings)
is here.
 A similar talk was presented at the
Australian Mathematical Society 55th Annual Meeting,
Wollongong, 28 September 2011.
34th ACCMCC, Canberra, 6 December 2010
ANU, 12 August 2010

Factoring Integers  an Introduction
(an introductory talk to given to year 11 students)
Overhead transparencies (beamer format):
[pdf]
CARMA Number Theory Workshop, Newcastle, NSW, 8 July 2010

Ramanujan and Euler's Constant (in memory of Edwin M. McMillan)
(invited talk presented at the
CARMA Number Theory Workshop,
University of Newcastle, NSW, 79 July 2010).
We discuss some formulas of Ramanujan that are relevant
to the computation of Euler's constant 0.577...,
recent record computations by Alexander Yee, and the contributions
of McMillan and Riemann.
Overhead transparencies (beamer format):
[pdf]
Hadamard Maximal Determinant Workshop, ANU, 14 May 2010

Decomposing Gram matrices,
(invited talk presented at the
Hadamard Maximal Determinant Workshop,
Australian National University, Canberra, 1317 May 2010).
We discuss algorithms to decompose Gram matrices in
order to find {+1,1} matrices of maximal determinant.
Overhead transparencies (beamer format):
[pdf]
CARMA Opening, Newcastle, NSW, 31 October 2009

The Great Trinomial Hunt
(invited talk presented at the opening of
CARMA, University of Newcastle, NSW, 31 October 2009).
This talk announced the successful completion of a search for primitive
trinomials whose degree is the exponent of a Mersenne prime
(at least until the
GIMPS Project finds another Mersenne prime).
Overhead transparencies (beamer format):
[pdf]
Longer talk given as an MSI Colloquium:
[pdf]
Queen Mary, London, 30 March 2009

Factoring and Testing Irreducibility of Sparse Polynomials
over Small Finite Fields
(seminar presented at
Queen Mary, University of London, 30 March 2009).
Overhead transparencies:
[pdf]
Christchurch, December 2008

Three Ways to Test Irreducibility
(presented at the Seventh Australia  New Zealand Mathematics
Convention
(ANZMC2008), Christchurch, New Zealand,
812 December 2008).
This talk announced the discovery of a new
primitive trinomial
of record degree 43112609.
Overhead transparencies:
[pdf]
 An updated version was presented at the
25th British Colloquium for Theoretical Computer Science
(BCTCS09), University of Warwick, 7 April 2009.
Overhead transparencies:
[pdf]
 A prelimininary version was presented at the
MASCOS annual conference
held in Beechworth, Victoria,
1011 July 2008).
Melbourne, July 2007

A Multilevel Blocking Distinct Degree Factorization Algorithm
(presented at the
Fq8 Conference
held in Melbourne,
913 July 2007).
Overhead transparencies:
[pdf]
 A similar talk was presented at the
University of Adelaide,
7 Dec 2007.
Stanford, March 2007
Canberra, February 2007
Canberra, October 2006

Pitfalls in Computation: Random and not so Random Numbers
( NAMS seminar,
ANU, 9 October 2006).
Overhead transparencies:
[pdf]
Berlin, July 2006

Using Magma to Find Good Xorshift Random Number Generators
(invited talk presented at the
Magma 2006 Conference,
Berlin, 30 July 2006).
Overhead transparencies:
[pdf]
 A similar talk was presented at
Sydney University,
14 June 2007.
Berlin, July 2006
Nancy, July 2006

Fast Algorithms for HighPrecision Computation of Elementary Functions
(invited talk presented at the
RNC7 Conference,
Nancy, France, 12 July 2006).
Overhead transparencies:
[pdf]
 A similar talk was presented at
Sydney University,
13 June 2007.
Townsville, July 2006

Some LongPeriod Random Number Generators using Shifts and Xors
(presented at the
CTAC06 Conference,
Townsville, 3 July 2006).
Overhead transparencies:
[pdf]
Canberra, September 2005

Challenges in Solving Large Sparse Linear Systems over Finite Fields
(Symposium on Optimisation and Data Analysis in honour of
Mike Osborne's 70th birthday),
Canberra, 23 September 2005).
Overhead transparencies:
[dvi]
[pdf]
[ps]
Oxford, February 2005

Computing Ratings from Eigenvectors
(Computational Mathematics and Applications Seminar,
Oxford, 3 February 2005).
Overhead transparencies:
[dvi]
[pdf]
[ps]
Paper: [pdf]
Oxford, November 2004
Lyngby, June 2004

Fast and Reliable Random Number Generators for Scientific Computing
(invited talk presented at the
PARA04 Workshop, StateoftheArt in Scientific Computing,
Lyngby, Denmark, 2023 June 2004).
Overhead transparencies:
[dvi]
[pdf]
[ps]
 Revision for AdvCom seminar, ANU, 8 May 2006:
[pdf]
[ps]
Banff, Clemson and Oxford, AprilJuly 2003
Montreal, May 2003

Random Number Generators with Period Divisible by a Mersenne Prime
(invited talk presented at the 2003 International Conference on
Computational Science and its Applications (ICCSA03),
Montreal, Canada, 21 May 2003).
Overhead transparencies:
[dvi]
[pdf]
[ps]

A paper on this topic is available.
Clemson, April 2003
Bath and Oxford, November 2002

Large Sparse Linear Systems over Finite Fields
(presented at Bath/RAL Numerical Analysis Day, 4 Nov 2002;
also Departmental Seminar, OUCL, Oxford, 12 Nov 2002;
updated version presented in Canberra, 23 September 2005).
Overhead transparencies:
[pdf]
[ps]
Hong Kong, September 2001

Primitive Trinomials and Random Number Generators
(distinguished lecture series seminar presented at
the Chinese University of Hong Kong in celebration of the
tenth Anniversary of the Faculty of Engineering, 26 Sept 2001).
Overhead transparencies:
[dvi]
[pdf]
[ps]
 Similar talks were given at

Some papers on these topics
are available.
Birmingham, Manchester and Utrecht, March  April 2001

Prospects for Integer Factorisation Algorithms
(seminar presented at Utrecht, 5 April 2001;
also Birmingham and Manchester, March 2001).
Overhead transparencies:
[dvi]
[pdf]
[ps]

Related talks were given in:
 For details, see the
survey paper presented
at COCOON 2000, Sydney, July 2000.
Symposium in Celebration of the Work of Tony Hoare, Oxford, Sept 1999

Twenty years' analysis of the binary Euclidean algorithm
(Hoare Symposium, Oxford, 15 Sept 1999).
Overhead transparencies:
[dvi]
[pdf]
[ps]
Related talks were given in:
 For more details, see the
paper which appeared in
the Hoare Symposium Proceedings.
Special Series of Lectures on Algorithms, Oxford, 1999

Six lectures on
algorithms
(Oxford, MayJune 1999)
Overhead transparencies:
[pdf]
[ps]
More details of each lecture.
Cambridge, May 1999

Fast and Numerically Stable Algorithms for Structured Matrices
(seminar,
DAMTP,
Cambridge University, May 1999).
Overhead transparencies:
[dvi]
[pdf]
[ps]
 For more details, see the
paper
which appeared as a chapter in
[preliminary version of a chapter which appeared in
Fast Reliable Algorithms for Matrices with Structure
(edited by Kailath and Sayed), SIAM, 1999, 103116].
Arith 14, Adelaide, April 1999
CWI Number Theory Day, Amsterdam, May 1998

Integer Factorization Algorithms Illustrated by the
Factorization of Fermat Numbers
(invited talk, Number Theory Day, CWI, Amsterdam, May 1998).
Overhead transparencies:
[dvi]
[pdf]
[ps]
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