Pierre-Louis Giscard

Maître de Conférences (Lecturer), Algebraic-Combinatorics
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville (LMPA)
Université Littoral Côte d'Opale, Calais

Tel: +33 3 21 46 55 84
Email: giscard@univ-littoral.fr

Research interests

My research is centered on the combinatorial and algebraic structures associated with walks (a.k.a. paths) on graphs and their applications throughout mathematics, but also in computer science and physics. My long term goal is to approach the long standing open problem of enumerating self-avoiding polygons on infinite regular lattices via a completely algebraic route, by extending techniques from number theory to walks. I am always keen on discussing research and participating in research collaborations on a wide variety of subjects, from quantum mechanics to applied network analysis.

I am the coordinator of the ANR (French National Research Agency) research project ALCOHOL (ALgebraic COmbinatorics of Hikes On Lattices)

Keywords : posets, Cartier-Foata monoids, self-avoiding walks, self-avoiding polygons, Hopf algebras
ORCID : 0000-0003-3025-8750
ResearchGate : here
Google scholar : here
Academia : here


All of my publications are available on the arXiv.

Raw data

Raw molecular data pertaining to the cationic tin oxo-cluster used in "General solutions for quantum dynamical systems driven by time-varying Hamiltonians: applications to NMR" arXiv 1905.04024, provided by Dr. F. Ribot, is available here
Molecular dynamics movies from the same work: Movie 1, Movie 2, Movie 3, Movie 4, Movie 5, Movie 6 and the colour bar


Counting simple cycles and simple paths on graphs
MATLAB versions:
For counting simple cycles of any length on any (weighted directed) graph: CycleCount
For counting simple paths of any length on any (weighted directed) graph: PathCount
For counting both simple cycles and simple paths at the same time: CyclePathCount
PYTHON versions: here

Machine learning on structured datasets
All-cycles and paths kernel for automatic graph classification tasks: here
Weisfeiler-Lehman optimal assignment on graphs (MATLAB): here
Weisfeiler-Lehman optimal assignment on graphs (JAVA): here

Loop-centrality on large networks
Algorithms determining the asymptotic fraction of network flows passing through selected loops (MATLAB): here and there.


Future presentation(s) and visit(s):

  • Short Talk by C. Bonhomme on a joint work, Theory of Solid State NMR: from Dyson, Magnus, Feynman to Path-Sum, Alpine Conference on Magnetic Resonance in Solids, 15-19th September 2019
  • Invited Talk, Fédération de Recherche Mathématique du Nord Pas de Calais, 15th October 2019

    Past presentations:

  • Contributed talk by Stefano Pozza (Charles University) on a joint work, Lanczos-like method for the time-ordered exponential, International Conference on Matrix Analysis and its Applications (MATTRIAD 2019), 9th September 2019, slides
  • Cambridge visit and meeting with Prof. Bonhomme, Prof. Pickard and Prof. Haydock; 15-17th July 2019
  • Stefano Pozza (Charles University), ULCO matrix analysis seminar on a joint work, Lanczos-like method for the time-ordered exponential, 25th June 2019, slides
  • Invited talk, Walk combinatorics: from number theory to quantum mechanics, ALEA Young 2019 workshop, 19-24 May 2019 Caen, slides
  • Contributed talk by C. Bonhomme on a joint work, A New Approach of Time-Ordered Exponential in NMR: the Path-Sum, 60th Experimental Nuclear Magnetic Resonance Conference, April 7-12, 2019, Pacific Grove, California, slides
  • Outreach, short presentation to high-schoolers Walking on graphs, 13 February 2019
  • Short scientific presentation Combinatoire algébrique des chemins, HCERES visit, 11 February 2019, slides
  • Invited seminar and short research stay, Networks analysis from number theoretic sieves : biological applications University of Strathclyde, 5-9 February 2019, slides
  • Seminar, Counting graph walks with sieves joint seminar University of Kent - Université du Littoral Côte d'Opale, 30 January 2019, slides
  • Seminars, Cribles et polygones auto-évitants I & II, Mathematics Department, Université du Littoral Côte d'Opale, 8 and 29 November 2018
  • Seminar, Une série pour la constante connective du réseau carré, Laboratoire d'informatique de l'École polytechnique (LIX), 21 November 2018
  • Contributed talk, Un crible non-commutatif en biologie, rencontres ALEA, CIRM Marseilles, March 2018, slides
  • Invited seminar, Théorie des chemins et informatique : interactions, Laboratoire d'Informatique Fondamentale, Université Aix-Marseilles, March 2018
  • Invited seminar, Des nouvelles de l'exponentielle ordonnée, Institut Mathématique de Bourgogne, Université de Bourgogne, March 2018, slides
  • Seminar, La théorie des chemins: une extension de la théorie de nombres, laboratoire Joseph Liouville, Université Littoral Côte d'Opale, January 2018
  • Extended visit to the University of Talca, Chile, group of Prof. María Ronco, November 2017.
  • Seminar, Introduction aux cribles : théorie des nombres & polygones auto- évitants, Laboratoire Bordelais de recherche en informatique (LaBRI), October 2017
  • Contributed Talk, Loop Centrality in Complex Economic and Biological Networks, Sixth International Conference on Complex Networks and their Applications, Lyon, November/December 2017
  • Invited seminar, La théorie des chemins. Une extension de la théorie des nombres et ses applications, Team SPOC, Laboratoire IMB (Univ. Bourgogne, Dijon, France), 27th September 2017, slides
  • Seminar, The theory of walks. An overview, Max Planck Institute for Informatics, Saarbrucken, July 2017, slides
  • Short presentation, Loop centrality in complex networks, CoSyDy meeting, Leeds UK, 25th July 2017
  • Short presentation, Extending number theory to walks on graphs, Journees ALEA, Centre International de Rencontres Mathématiques (CIRM), Marseilles, France, 20-24 March 2017, slides
  • Invited seminar, Cycle Counting: Theory and Applications, Stochastic Processes Group, University College London, United Kingdom, 8th March 2017slides
  • International Summer School on Complex Networks, Bertinoro, Italy, 11-15th July 2016
  • Invited seminar, Network Cluster Lecture, Extending number theory to walks on graphs: why? how? and so what?, Keble College Advanced Studies Centre, Oxford, UK, 25th April 2016, slides
  • Invited seminar given by P. Rochet, Walks are just connected hikes, University of Antofagasta, Chile, 26th November 2015, slides
  • Seminar, Of walks and graphs: an introduction to walk theory, University of York, UK, 15th October 2015, slides
  • Invited seminars, Walk Theory I & II , University of Geneva, Switzerland, September 2014, slides: talk 1, talk 2
  • Invited seminar, Walk theory, with applications, Said Business School, Oxford, UK, 14th August 2014, slides
  • Network journal club seminar, Of Walks and Graphs, An Introduction to Walk Theory, Department of Mathematics, Oxford, UK, 16th July 2014, slides
  • Atomic and Laser Physics Seminar, Walk Theory, Oxford, UK, 9th June 2014, slides
  • Poster presented by S. Thwaite, Evaluating Matrix Functions by Resummations on Graphs: the method of walk-sums", Computational methods for quantum materials, Sherbrooke, Canada, June 2014, poster
  • Poster presentation, The method generating theorem, Workshop on Advances in Matrix Functions and Matrix Equations, University of Manchester, UK, March 2013, e-poster
  • Invited seminar, Evaluating Matrix Functions by Resummations on Graphs: the Method of Path-Sums, Numerical Analysis Group, Department of Mathematics, Oxford, UK, November 2012, slides
  • Invited seminar, Matrix functions as continued fractions, Numerical Linear Algebra Group, Department of Mathematics, University of Manchester, UK, October 2012, slides
  • Poster, The walk-sum and path-sum methods for simulating quantum many-body systems, International congress on mathematical-physics, Aalborg, Denmark, August 2012, e-poster
  • Contributed presentation, Evaluating Matrix Functions by Resummations on Graphs: the Method of Path-Sums, SIAM Conference on applied linear algebra, Valencia, Spain, June 2012, slides
  • Poster, Walk-sum, a new approach to quantum evolutions, Windsor workshop on dynamics and simulation of ultra-cold matter, Windsor, UK, August 2011
  • Atomic and Laser Physics Seminar, The Theory of Operator-Lattices A New Analytical Tool for Quantum Many-Body Physics, Oxford, UK, September 2010, slides
  • Poster, An Analytical Tool for Quantum Many-Body Physics, Les Houches physics summer school, Les Houches, France, July 2010
  • Presentation by E. Wright, Long distance beam propagation in colloidal suspensions: comparison between theory and experiment, SPIE Optics and Photonics, San Diego, USA, August 2008
  • Poster, Entanglement of a Laguerre-Gaussian cavity mode with a rotating mirror, DAMOP, Pennsylvania State College, USA, May 2008

  • Teaching / Enseignement

  • Cours de Maths 1 pour les étudiants de L1 MSPI
  • Cours de Maths 3 pour les étudiants de L1 MSPI
  • Cours de Maths 2 pour les étudiants de L2 STS Physique-Chimie


  • I taught quantum mechanics and mathematical-physics to both mathematics and physics students in Keble and Somerville colleges, Oxford (2010-2015)
  • I was an interviewer at the Oxford interviews for applicants to the Mathematics course at Keble college (2014)
  • I taught Numerical Analysis at the University of York (2016-2017)
  • Short bio

    I completed two MSc degrees from the University of Arizona and Institut d'Optique Graduate School in 2009 (Diplôme d'Ingénieur). That same year I was awarded a Scatcherd European scholarship to fund my DPhil in mathematical-physics from Keble College, Oxford, which I completed in 2014 under the direction of Prof. Dieter Jaksch. I received a University of Oxford Thesis Prize for my thesis "A graph theoretic approach to matrix functions and quantum dynamics".

    Following my DPhil, I held a postdoc position at Oxford funded by the successful EPSRC Grant EP/K038311/1 obtained together with Prof. Jaksch, Dr. Stephen Clark and Dr. Sarah Al-Assam. In 2015, I was awarded a three years Research Fellowship by the Royal Commission for the Exhibition of 1851 and chose to undertake it in the group of Prof. Richard Wilson, at the University of York.

    I am a lecturer (Maître de Conférences) of algebraic combinatorics at the Université du Littoral Côte d'Opale, since September 2018.
    My full CV is available here.