Richard Brent - Some Talks and Lectures

One-Day Seminar on Inverse Problems, April 2012

• Inverse problems, cryptography and security
  (presented at the Second One-Day 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

• On the distribution of arg(zeta(sigma+it)) in the half-plane sigma > 1/2
  (presented at the International Number Theory Conference in Memory of Alf van der Poorten, Newcastle, NSW, 12-16 March 2012).
  We quantify the statement that the real part of the Riemann zeta function is "usually positive".
  (Joint work with Juan Arias de Reyna and Jan van de Lune.)
  Overhead transparencies (beamer format): [pdf]
  
• A longer version: On the sign of the real part of the Riemann zeta function
  was presented at the Workshop on Number Theory and its Applications in Memory of Alf van der Poorten, Macquarie University, Sydney, 19-20 March, 2012.
  Overhead transparencies (beamer format): [pdf]
  

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, 28-30 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]
  

Workshop in Honour of Jon Borwein, Simon Fraser University, Canada, 16-20 May 2011

• Computing Bernoulli and Tangent numbers
  (presented via video-link from Newcastle for the Computational and Analytical Mathematics Conference in Honour of Jonathan Borwein's sixtieth birthday, 16-20 May, 2011).
  We consider some algorithms for computing Bernoulli, Secant and Tangent numbers, giving both asymptotically fast algorithms and convenient algorithms based on three-term recurrences.
  Video of the talk.
  Overhead transparencies (beamer format): [pdf]
  

ACCMCC, Canberra, 6 December 2010

• An O(M(n) log n) algorithm for the Jacobi symbol
  (presented at the 34th ACCMCC Conference, ANU, 6 December 2010).
  We give an O(M(n) log n) algorithm for computing the Jacobi symbol, based on the binary recursive GCD algorithm of Stehlé and Zimmermann.
  Overhead transparencies (beamer format): [pdf]
  A similar talk (presented by my co-author Paul Zimmermann at the ANTS-IX Conference, INRIA, Nancy, France, 20 July 2010).
  Overhead transparencies (beamer format): [pdf]
  A related paper is here.
  

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, 7-9 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, 13-17 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]
  

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, 8-12 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, 10-11 July 2008).
  

Melbourne, July 2007

• A Multi-level Blocking Distinct Degree Factorization Algorithm
  (presented at the Fq8 Conference held in Melbourne, 9-13 July 2007).
  Overhead transparencies: [pdf]
  
• A similar talk was presented at the University of Adelaide, 7 Dec 2007.
  

Stanford, March 2007

• George Forsythe's Last Paper
  (presented at the Stanford 50 Conference held at Stanford University, 29-31 March 2007).
  Overhead transparencies: [pdf]
  Paper: [pdf]
  

Canberra, February 2007

• The Myth of Equidistribution for High-Dimensional Simulation
  (presented at the Second Workshop on High-Dimensional Approximation, ANU, 19 February 2007).
  Overhead transparencies: [pdf]
  Paper: [pdf]
  

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

• Reversible Rotations, or how Rho Lost its Tail
  (keynote talk presented at the Computing by the Numbers: Algorithms, Precision, and Complexity Workshop, Berlin, 20-21 July 2006).
  Overhead transparencies: [pdf]
  

Nancy, July 2006

• Fast Algorithms for High-Precision 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 Long-Period 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

• Uncertainty can be Better than Certainty: Some Algorithms for Primality Testing
  (28th Strachey Lecture, Oxford, 2 November 2004).
  Overhead transparencies: [dvi] [pdf] [ps]
  
• Revision for Computational Mathematics seminar, MSI, ANU, 27 November 2006: [pdf] [ps]
  
• Revision for talk to the ANU Mathematics Society, 3 March 2010: [pdf]
  

Lyngby, June 2004

• Fast and Reliable Random Number Generators for Scientific Computing
  (invited talk presented at the PARA04 Workshop, State-of-the-Art in Scientific Computing,
  Lyngby, Denmark, 20-23 June 2004).
  Overhead transparencies: [dvi] [pdf] [ps]
  
• Revision for AdvCom seminar, ANU, 8 May 2006: [pdf] [ps]
  

Banff, Clemson and Oxford, April-July 2003

• Almost Irreducible and Almost Primitive Trinomials
  (invited talk presented at the Hugh Williams 60-th birthday conference, Banff, Canada, 26 May 2003).
  Overhead transparencies: [dvi] [pdf] [ps]
  A revised version of this talk was presented at the
  • 22nd Secants meeting, Royal Holloway, University of London (29 November 2003).
  Another version of this talk was presented at
  • Laboratoire STIX, École Polytechnique, Palaiseau, France (10 December 2003).
• Primitive and Almost Primitive Trinomials over GF(2)
  (invited talk presented at the East Coast Computer Algebra Day, Clemson, South Carolina, 5 April 2003).
  Overhead transparencies: [dvi] [pdf] [ps]
  A related talk was given at
  • UKCRC Algorithms and Complexity Day, University of Warwick (3 May 2002).
• All You Wanted to Know about Irreducible and Primitive Trinomials
  (a 20-minute introduction to the subject, Oxford Supercomputer Centre Mini-Conference, 1 July 2003).
  Overhead transparencies: [dvi] [pdf] [ps]
  
• Some papers on these topics are available.
  

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

• Primality Testing
  (seminar presented at Clemson University, South Carolina, 4 April 2003).
  Overhead transparencies: [dvi] [pdf] [ps]
  
• A revised version of this talk was presented to the Oxford University Invariant Society (25 November 2003).
• A preliminary version of this talk was given in a research seminar at the Oxford University Computing Laboratory (18 October 2002).
  
• A similar talk was given at a Monash University Intelligent Systems seminar (15 August 2006).
  
• See also Strachey Lecture above.
  

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
  • Bristol (23 Oct 2001);
  • Oxford (1 May 2001) and INRIA Lorraine (6 Sept 2001);
  • CWI, Amsterdam (6 April 2001);
• 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:
  • Hong Kong and INRIA Lorraine, September 2001
  • Zurich, December 2000
  • Sydney (COCOON), July 2000
  • Cardiff, November 1999
  • Toulouse (Europar), September 1999
• 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:
  • Hong Kong, Sept 2001;
  • Warwick, June 1998.
• 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, May-June 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, 103-116].

Arith 14, Adelaide, April 1999

• Computer arithmetic - a programmer's perspective
  (invited talk, 14th IEEE Symposium on Computer Arithmetic, Adelaide, April 1999).
  Overhead transparencies: [dvi] [pdf] [ps]
  

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]
  

Return to Richard Brent's index page