Research Activities

My main interest is exact linear algebra algorithms and the underlying arithmetic. One of my primary interests is the analysis of algorithms and the development of the best suited implementations. This includes problems over finite fields such as finding minimal polynomial of matrices and every problem related to, but also problems over the integers like solving systems of linear equations. The development and the maintaining of the "LinBox" library, which is the concretisation of an international joined work around exact linear algebra, remain also two majors objectives in my research.

Publications

Articles in journals and refereed conference proceedings

• P. Giorgi, L. Imbert and T. Izard. Parallel modular multiplication on multi-core processors.
  Proc. ARITH 21: IEEE Symposium on Computer Arithmetic, Austin, Texas, USA, April 2013.
• P. Giorgi. On Polynomial Multiplication in Chebyshev Basis.
  IEEE Transactions on Computers, Volume 61, number 6, pp. 780--789, June 2012.
• B. Boyer, J.-G. Dumas and P. Giorgi. Exact Sparse Matrix-Vector Multiplication on GPU's and Multicore Architectures.
  Proc. PASCO'10: Parallel Symbolic Computation, Grenoble, France, July 2010.
• P. Giorgi, T. Izard and A. Tisserand. Comparison of Modular Arithmetic Algorithms on GPUs.
  Proc. ParCo'09: International Conference on Parallel Computing, September 2009, Lyon, France.
• P. Giorgi, L. Imbert and T. Izard. Optimizing elliptic curve scalar multiplication for small scalars.
  Proc. Mathematics for Signal and Information Processing in SPIE'09, Volume 7444, August 2009, San Diego, CA, USA.
• J.-G. Dumas, P.Giorgi and C. Pernet. Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages.
  ACM Transactions on Mathematical Software, Volume 35, number 3, pp. 19:1--19:42, October 2008.
• S. Boldo, M. Daumas and P. Giorgi. Formal proof for delayed finite field arithmetic using floating point operators.
  Proc. RNC'8: 8th Conference on Real Numbers and Computers, July 2008, Santiago de Compostela, Spain.
• P. Giorgi, C. Nègre and T. Plantard. Subquadratic Binary Field Multiplier in Double Polynomial System.
  Proc. SECRYPT'2007: International Conference on Security and Cryptography, Barcelona, Spain, July 2007.
• J.-G. Dumas, P. Elbaz-Vincent, P. Giorgi and A. Urbanska. Parallel Computation of the rank of large sparse matrices from algebraic K-theory.
  Proc. PASCO'2007: Parallel Symbolic Computation, London, Ontario, Canada, July 2007.
• W. Eberly, M. Giesbrecht, P. Giorgi, A. Storjohann and G. Villard. Faster Inversion and other Black Box Matrix Computation Using Efficient Block Projections.
  Proc. ISSAC'07: International Symposium on Symbolic and Algebraic Computation, Waterloo, Ontario, Canada, pages 143--150, July 2007, ACM Press, New York.
• W. Eberly, M. Giesbrecht, P. Giorgi, A. Storjohann and G. Villard. Solving Sparse Rational Linear Systems.
  Proc. ISSAC'06: International Symposium on Symbolic and Algebraic Computation, Genova, Italy, pages 63-70, July 2006, ACM Press, New York.
• J.-G. Dumas, P.Giorgi and C. Pernet. FFPACK: Finite field linear algebra package.
  Proc. ISSAC'04: International Symposium on Symbolic and Algebraic Computation , Santander, España, pages 119-126, July 2004, ACM Press, New York.
• P. Giorgi, C.-P. Jeannerod and G. Villard. On the complexity of polynomial matrix computations.
  Awarded with distinguished student author award
  Proc. ISSAC'03: International Symposium on Symbolic and Algebraic Computation , Philadelphia, Pennsylvania USA, page 135-142, August 2003, ACM Press, New York.
• J.-G. Dumas, T. Gautier, M. Giesbrecht, P. Giorgi, B. Hovinen, E. Kaltofen, B.D. Saunders, W.J. Turner and G. Villard. LinBox: A Generic Library for Exact Linear Algebra.
  Proc. ICMS'02: International Congress of Mathematical Software, Beijing, China, pages 40-50, August 2002, World Scientific, Singapore.

Research reports

• P. Giorgi, L. Imbert and T. Izard. Multipartie Modular Multiplication. August 2011.
  

Posters

• Implementation of a Las Vegas Integer Matrix Determinant Algorithm, (in ppt )
  ECCAD'05: East Coast Computer Algebra Day (Ashland, USA-Ohio, March 2005)
• LUdivine: A Symbolic block LU factorisation for matrices over finite fields using BLAS,
  ECCAD'03: East Coast Computer Algebra Day (Clemson, USA-South Carolina, April 2003)

Dissertations

• PhD dissertation (advisor: G. Villard)
  Arithmetic and algorithmic in exact linear algebra for the LinBox library (in french).
  Ecole Normale superieure de Lyon, LIP, Lyon, France, December 2004.
  (PDF, PS)
• MSc dissertation (advisor: Pr. J.-C. Bajard )
  Study in RNS basis change (in french)
  Universite Montpellier II, LIRMM, Montpellier, France, July 2001.

Talks

• On Polynomial Multiplication Complexity in Chebyshev Basis,
  Seminaire Algorithmes INRIA, INRIA Rocquencourt (Roquencourt, France, November 29 2010)
  Seminaire Arenaire, LIP - ENS Lyon (Lyon, France, June 17 2010)
• Arithmétique modulaire entière en base polynomiale (in french),
  Seminaire CASYS-BIBOP, LJK - Université Joseph Fourier (Grenoble, France, March 15 2007)
• Theory and Practice for Solving Sparse Rational Linear Systems (in french),
  Seminaire LIRMM, département informatique (Montpellier, France, March 8 2007)
• LinBox: évolutions et interactions d'une bibliothèque d'algèbre linéaire exacte (in french),
  Journées Nationales de Calcul Formel 2007 (Luminy, France, February 1, 2007)
• Solving Sparse Rational Linear Systems,
  ISSAC'06: International Symposium on Symbolic and Algebraic Computation (Genova, Italy, July 9-12 2006)
• Solving sparse integer linear systems ,
  Séminaire MOSAIC, laboratoire LMC-IMAG (Grenoble, France, June 21 2006)
  Séminaire DALI, laboratoire LP2A-Perpignan (Perpignan, France, June 27 2006)
• An interface to link the LinBox library to Maple (invited talk),
  ORCCA - Joint Lab Meeting (Waterloo, Canada, October 14 2005)
• Integer linear system solving (invited talk),
  Challenge in Linear and Polynomial Algebra in Symbolic Computation Software (Banff, Canada, October 1-6 2005)
• On the use of polynomial matrix approximant in the block Wiedemann algorithm (invited talk),
  Canadian Mathematical Society meeting (Waterloo, Canada, June 5-7 2005)
• Calculs haute performance en algèbre linéaire exacte ,
  Séminaire CALFOR, laboratoire LIP6-Université Paris VI (Paris, France, May 10 2005)
• Aritmétique et algorithmique en algèbre linéaire exacte pour la bibliothèque LinBox,
  Soutenance de thèse LIP-ENS Lyon (Lyon, France, December 20 2004)
• LinBox: une bibliothèque générique pour l'algèbre linéaire exacte,
  Ecole Jeunes Chercheurs en Algorithmique et Calcul Formel (Grenoble, France, March 29 - April 2 2004)
• LinBox: algèbre linéaire exacte sur les corps finis et applications,
  Séminaire MOSAIC, laboratoire LMC-IMAG (Grenoble, France, March 25 2004)
• From BLAS routines to finite field exact linear algebra solutions, (invited talk)
  ACA'03 : Application on Computer Algebra (Raleigh, USA-North Carolina, July 28-31 2003)
• LinBox: présentation générale et solutions génériques pour l'algèbre linéaire,
  Journée Nationale de Calcul Formel (Luminy, France, January 20-24 2003)
• LinBox: a generic library for exact linear algebra,
  Workshop on open source computer algebra (Lyon, France, May 21-23 2002)\
• Arithmétique des corps finis dans la bibliothèque LinBox,
  Journées Arinews (Paris, France, January 23-24 2002)
• Étude des changements de base en RNS,
  Soutenance de DEA LIRMM-Université Montpellier II (Montpellier, France, July 2001)

Projects & Softwares

• FFLAS-FFPACK, finite field linear algebra subroutines/package home page
• Givaro, a C++ library for computer algebra home page
• LinBox joint CNRS/NSF project on exact linear algebra home page
• Roxane Reliable Open Software-Components for Algebraic and Numeric Efficiency home page
• Ocam Opérateurs Cryptographiques et Arithmétique Matérielle home page

Link to others softwares ...

Collaborators

• IMAG-LJK, Grenoble: Jean-Guillaume Dumas
• LIG, Grenoble: Clément Pernet
• University of Waterloo: Georges Labahn, Mark Giesbrecht, Arne Storjohann
• University of Calgary: Wayne Eberly
• LIP-ENS, Lyon: Claude-Pierre Jeannerod, Gilles Villard
• DALI, Perpignan: Christophe Nègre
• IRISA, Lannion: Arnaud Tisserand

PhD Students

• 2008-2011: Thomas Izard on software development for efficient arithmetic in cryptography

Others Activities

• Organization of the Computer Algebra session during the french national workshop RAIM 2008 at Université des Sciences et Technologies de Lille, June, 2008, 42 participants.
• In charge of proceedings (papers and electronic version) for colloquium Perpi'2006 gathering conferences RenPar'17 / SympA'2006 / CFSE'5 / JC'2006
• Software Exhibition Chair at the International Symposium on Symbolic and Algebraic Computation 2006 - ISSAC'06
• Organization of the French national workshop Journées Arinews et AS arithmétique at ENS-Lyon, November 2003, 36 participants

Pascal Giorgi Last modified: Thu Sep 1 15:03:44 CEST 2011