Publications

Publications in journals
All are available on
the arXiv in open access
 A copreLie structure from chronological loop erasure in graph walks
L. Foissy, P.L. Giscard, C. Mammez
Preprint
Open access link (2023)
 Exact solutions for the timeevolution of quantum spin systems under arbitrary waveforms using algebraic graph theory
P.L. Giscard, M. Foroozandeh
Computer Physics Communications, 2022, p. 108561, doi: 10.1016/j.cpc.2022.108561
Journal link, open access link (2022)
 Realizable cycle structures in digraphs
J. Fromentin, P.L. Giscard, T. Karaboghossian
European Journal of Combinatorics, Vol. 113, 103748 (2023), doi: 10.1016/j.ejc.2023.103748. Journal link, open access link (2023)
 Computations of general Heun functions from their integral series representations
T. Birkandan, P.L. Giscard, A. Tamar
2021 Days on Diffraction (DD), 2021, pp. 1218, doi: 10.1109/DD52349.2021.9598600.
Journal link, open access link (2021)
 Elementary Integral Series for Heun Functions. With an Application to BlackHole Perturbation Theory
P.L. Giscard, A. Tamar
Editor's pick at Journal of Mathematical Physics, Vol.63, Issue 6: 063501 (2022).
Journal link, open access link.
 Asymptotic counts for the walk multiples of selfavoiding polygons on lattices using sieves
P.L. Giscard
Discrete Mathematics 344(4): 112305, doi 10.1016/j.disc.2021.112305, (2021).
Journal link, open access link.
 Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczoslike method
P.L. Giscard, S. Pozza
Linear Algebra and Its Application 624: 153173, (2021)
Journal link, open access link.
 Lanczoslike algorithm for the timeordered exponential: the *inverse problem
P.L. Giscard, S. Pozza
Applied Mathematics, 121, doi 10.21136/AM.2020.034219, (2020).
Journal link, open access link.
 On the solutions of linear Volterra equations of the second kind with sum kernels
P.L. Giscard
Journal of Integral Equations and Applications, 32(4): 429455 (2020).
Journal link, open access link.
 A Lanczoslike method for nonautonomous linear ordinary differential equations
P.L. Giscard, S. Pozza
Bollettino dell'Unione Matematica Italiana, 21982759 (2022).
Journal link, open access link (2022)
 Dynamics of quantum systems driven by timevarying Hamiltonians: Solution for the BlochSiegert Hamiltonian and applications to NMR
P.L. Giscard, C. Bonhomme
Physical Review Research 2, 023081 (2020)
Journal link, open access link
 Computing Optimal Assignments in Linear Time for Approximate Graph Matching
N. M. Kriege, P.L. Giscard, F. Bause, R. C. Wilson
2019 IEEE International Conference on Data Mining (ICDM), Beijing, China, 2019, pp. 349358, (2019).
Journal link, open access link.
 A general purpose algorithm for counting simple cycles and simple paths of any length
P.L. Giscard, N. M. Kriege, R. C. Wilson
Algorithmica 81 (7), 27162737 (2019)
Journal link , open access link.
 Enumerating simple paths from connected induced subgraphs
P.L. Giscard, P. Rochet
Graphs and Combinatorics 34(6): 11971202, (2018).
Journal link, open access link.
 A Centrality Measure for Cycles and Subgraphs II
P.L. Giscard, R. C. Wilson
Applied Network Science 3(1): 9, (2018).
Journal link, open access link.
 The AllPaths and Cycles Graph Kernel
P.L. Giscard, R. C. Wilson
Open access link
 CycleCentrality in Economic and Biological Networks
P.L. Giscard, R. C. Wilson
Complex Networks & Their Applications VI (Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M., eds.), Springer International Publishing, 1428, (2018).
Journal link, open access link.
 A Hopf algebra for counting cycles
P.L. Giscard, P. Rochet, R. C. Wilson
Discrete Mathematics, volume 341:14391448 (2018).
Journal link, open access link.
 Evaluating balance on social networks from their simple cycles
P.L. Giscard, P. Rochet, R. C. Wilson
Journal of Complex Networks, volume 5: 750775 (2017).
Journal link, open access link.
 On Valid Optimal Assignment Kernels and Applications to Graph Classification
N. M. Kriege, P.L. Giscard, R. C. Wilson
Proceedings of the 30th International Conference on Neural Information Processing Systems, 16231631, (2016).
Journal link, open access link.
 Algebraic combinatorics on trace monoids: extending number theory to walks on graphs
P.L. Giscard, P. Rochet
SIAM Journal on Discrete Mathematics, volume 31: 14281453, (2017).
Journal link, open access link.
 Exact Inference on Gaussian Graphical Models of Arbitrary Topology using PathSums
P.L. Giscard, Z. Choo, S. J. Thwaite, D. Jaksch
Journal of Machine Learning Research, volume 17: 119 (2016).
Journal link, open access link.
 An Exact Formulation of the TimeOrdered Exponential using PathSums
P.L. Giscard, K. Lui, S. J. Thwaite, and D. Jaksch
Journal of Mathematical Physics, 56(5):053503 (2015).
Journal link, open access link.
 A Graph Theoretic Approach to Matrix Functions and Quantum Dynamics
P.L. Giscard
PhD Thesis, Keble College, University of Oxford, link (2014)
Mathematical, Physical and Life Sciences division, University of Oxford Thesis Commendation, Thesis Prize
 Evaluating Matrix Functions by Resummations on Graphs: the Method of PathSums
P.L. Giscard, S. J. Thwaite, D. Jaksch
SIAM Journal on Matrix Analysis and Applications, 34(2):445469 (2013).
Journal link, open access link.
 WalkSums, Continued Fractions and Unique Factorisation on Digraphs
P.L. Giscard, S. J. Thwaite, D. Jaksch
Open access link (2012)
 Optomechanical control of atoms and molecules
M. Bhattacharya, S. Singh, P.L. Giscard, P. Meystre
Laser Physics, 20(1):5767, (2010)
Journal link.
 Entangling the rovibrational modes of a macroscopic mirror using radiation pressure
M. Bhattacharya, P.L. Giscard, P. Meystre
Phyical Review A, 77:030303, (2008)
Journal link, open access link.
 Entanglement of a LaguerreGaussian cavity mode with a rotating mirror
M. Bhattacharya, P.L. Giscard, P. Meystre
Physical Review A, 77:013827 (2008).
Journal link, open access link.
 Long distance beam propagation in colloidal suspensions: comparison between theory and experiment
E. M. Wright, W. M. Lee, P.L. Giscard, K. Dholakia
Proceedings of SPIE  The International Society for Optical Engineering Volume 7038, 70380P (2008).
Journal link.
Unpublished papers, mostly produced during my MSc:
 An Explicit Bound for Dynamical Localisation in an Interacting ManyBody System, link
 The walksum method for simulating quantum manybody systems, link
 Tunable Supersolids of Rydberg Excitations Described by Quantum Evolutions on Graphs, link
 Quantum Mechanical Limits to Inertial Mass Sensing by Nanomechanical Systems, link
 Operators for the AharonovAnandan and SamuelBhandari Phases, link
 Considerations about the AharonovAnandan Phase for Time Independent Hamiltonians, link
 Optical squeezing of a mechanical oscillator by dispersive interaction, link
Abstracts published in peerreviewed conferences:
 Ultrafast convergent analytical solutions of the Bloch equations: the PathSum approach
C. Bonhomme, P.L. Giscard
62nd Experimental Nuclear Magnetic Resonance Conference (2021).
 Undamped and Damped Bloch Equations: Exact Solutions by PathSum
C. Bonhomme, P.L. Giscard
61st Experimental Nuclear Magnetic Resonance Conference, Baltimore, Maryland, (2020).
 Theory of Solid state NMR: from Dyson, Magnus, Feynman to PathSum
C. Bonhomme, P.L. Giscard
Alpine Conference on Magnetic Resonance in Solids (2019).
 A New Approach of Ordered Exponential in NMR: the PathSum
C. Bonhomme, P.L. Giscard
60th Experimental Nuclear Magnetic Resonance Conference, (2019).
Online articles for math popularization:
 Que saiton compter sur un graphe ? Partie 3: Matrices et chemins
P.L. Giscard, Image des Maths, link, December 2020
 Que saiton compter sur un graphe ? Partie 2: Motifs et polygones
P.L. Giscard, Image des Maths, link, October 2020
 Que saiton compter sur un graphe ? Partie 1: Des graphes du monde qui nous entoure
P.L. Giscard, Image des Maths, link, July 2020

Seminars

Future presentation(s) and visit(s):
Past presentations:
 Prague Workshop on Numerical Mathematics, invited presentation and research stay, link, July 2023
 Seminars by M. Ryckebusch on a joint work, Between graph theory and differential equations: the *product, Amiens (March 2023) and Calais (May 2023), presentation and slides.
 Seminar by T. Karaboghossian on a joint work, Why walks lead us astray in the study of graphs, Calais, 16th December 2021, slides.
 Invited presentation, A Lanczoslike algorithm for timeordered exponentials, 8th European Congress of Mathematics, Portorož, Slovenia, 21st June 2021, slides.
 T. Birkandan, P.L. Giscard, A. Tamar, A Python implementation of the general Heun function
using elementary integral series, Contributed presentation Days on Diffraction 2021, May 31 – June 4, 2021 St. Petersburg, slides and recorded presentation, starting from 39:30.
 Alcohol Workshop on walk combinatorics (WACA days), 2528 May 2021
 Contributed presentation by C. Bonhomme on joint research, Hydroxyapatite revisited by DNP and spin diffusion: Natural abundance 43Ca DNP MAS and ultrahigh magnetic field (35T) 43Ca experiments, modeling and new mathematical treatment of DNP process, American Chemical Society Spring 2021 meeting, April 516 2021, slides
 Contributed presentation by C. Bonhomme on joint research, Ultrafast convergent analytical solutions of the Bloch equations: the PathSum approach, Experimental Nuclear Magnetic Resonance Conference ENC 2021, March 2931 2021, slides
 Invited seminar, Dénombrement des polygones autoévitants: la route déterministe, Institut de Recherche Mathématique Avancée, Strasbourg, France, 18th February 2021, slides
 Invited seminar, Unexpected applications of walk combinatorics, Laboratoire Paul Painlevé, Université de Lille, 31st January 2020, slides
 Official presentation of the ANR ALCOHOL research project, Agence Nationale de la Recherche, Paris, 13th November 2019, slides
 Invited Talk, Combinatoire des chemins. De la théorie des nombres à la mécanique quantique, Fédération de Recherche Mathématique du Nord Pas de Calais, 15th October 2019, slides
 Short Talk by C. Bonhomme on a joint work, Theory of Solid State NMR: from Dyson, Magnus, Feynman to PathSum, Alpine Conference on Magnetic Resonance in Solids, 1519th September 2019, slides
 Contributed talk by Stefano Pozza (Charles University) on a joint work, Lanczoslike method for the timeordered 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; 1517th July 2019
 Stefano Pozza (Charles University), ULCO matrix analysis seminar on a joint work, Lanczoslike method for the timeordered exponential, 25th June 2019, slides
 Invited talk, Walk combinatorics: from number theory to quantum mechanics, ALEA Young 2019 workshop, 1924 May 2019 Caen, slides
 Contributed talk by C. Bonhomme on a joint work, A New Approach of TimeOrdered Exponential in NMR: the PathSum, 60th Experimental Nuclear Magnetic Resonance Conference, April 712, 2019, Pacific Grove, California, slides
 Outreach, short presentation to highschoolers 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, 59 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 autoévitants 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 noncommutatif en biologie, rencontres ALEA, CIRM Marseilles, March 2018, slides
 Invited seminar, Théorie des chemins et informatique : interactions, Laboratoire d'Informatique Fondamentale, Université AixMarseilles, 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, slides
 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, 2024 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, 1115th 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 walksums", 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, eposter
 Invited seminar, Evaluating Matrix Functions by Resummations on Graphs: the Method of PathSums, 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 walksum and pathsum methods for simulating quantum manybody
systems, International congress on mathematicalphysics, Aalborg, Denmark, August 2012, eposter
 Contributed presentation, Evaluating Matrix Functions by Resummations on Graphs: the
Method of PathSums, SIAM Conference on applied linear algebra, Valencia, Spain, June 2012, slides
 Poster, Walksum, a new approach to quantum evolutions, Windsor
workshop on dynamics and simulation of ultracold matter, Windsor, UK, August 2011
 Atomic and Laser Physics Seminar, The Theory of OperatorLattices
A New Analytical Tool for Quantum ManyBody Physics, Oxford, UK, September 2010, slides
 Poster, An Analytical Tool for Quantum ManyBody 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 LaguerreGaussian cavity mode with a rotating
mirror, DAMOP, Pennsylvania State College, USA, May 2008
