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data-btn-type="primary" data-btn-size="sm" data-btn-disabled="1">Defences</span> </div> </p> <div style='display:none'><div class="wrap_right plugin_wrap"> <p> <span class="bs-wrap bs-wrap-button" data-btn-type="default"><a href="https://www.irif.fr/admindb/seminaires/" class="urlextern" title="https://www.irif.fr/admindb/seminaires/" rel="ugc nofollow">Manage defences</a></span> </p> </div></div></div> <h2 id="habilitation_defences" class=" page-header pb-3 mb-4 mt-5">Habilitation defences</h2> <div class="level2"> <p> The <a href="http://www.irif.fr/_media/ical/hdr.ics" class="urlextern" title="http://www.irif.fr/_media/ical/hdr.ics" rel="ugc nofollow">calendar</a> of events (iCal format). <br/> In order to add the event calendar to your favorite agenda, subscribe to the calendar by using this link. </p> </div> </div></div> <p> <br/> </p> <h3 class="sectionedit3 page-header pb-3 mb-4 mt-5" id="next_talk">Next talk</h3> <div class="level3"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Friday December 6, 2024, 1PM, Salle 2011 (Sophie Germain)<br/> <strong>Sam Van Gool</strong> (IRIF) <em>Logical reflections: Profinite monoids, propositional quantifiers, and temporal operators</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3542"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3542"><div class="bs-wrap bs-wrap-well well well-sm"> My HDR manuscript surveys some of the research in algebra, topology, logic, and the foundations of computer science that I have contributed to since completing my PhD in 2014, and suggests directions for further research in this field. The work I report on falls into three research themes: (1) profinite monoids and their relationship to automata and regular languages; (2) uniform interpolation and its relationship to model-complete theories; (3) axiomatization and unifiability for temporal logics. A thematic coherence between these topics lies in the recurring appearance of techniques from infinite model theory and universal algebra for studying finitary phenomena, and the use of projective limits of finite structures. This report aims to show how these techniques help with solving problems in all three of these, a priori different, research themes. <p> The defense will be followed by drinks at IRIF, on the 4th floor of the same building. </p> <p> The manuscript is available via: <a href="https://www.samvangool.net/hdr.html" class="urlextern" title="https://www.samvangool.net/hdr.html" rel="ugc nofollow">https://www.samvangool.net/hdr.html</a> </div> </p> </div> <p> <br/> </p> </div> <h3 class="sectionedit4 page-header pb-3 mb-4 mt-5" id="previous_talks">Previous talks</h3> <div class="level3"> <p> <br/> </p> </div> <h4 id="year_2024">Year 2024</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2024" id="plugin_include__en__seminaires__hdr__hdr2024"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Wednesday March 20, 2024, 10AM, Amphithéâtre Turing, bâtiment Sophie Germain<br/> <strong>Geoffroy Couteau</strong> (IRIF) <em>Correlated Pseudorandomness in Secure Computation</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3543"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3543"><div class="bs-wrap bs-wrap-well well well-sm"> The focus of this habilitation thesis is on secure computation, an area of cryptography that lets multiple parties distributively compute a function on their private data. After providing a high-level introduction to my work in cryptography, the manuscript provides a gentle introduction to secret-sharing-based secure computation, which is aimed at a general audience. Then, the last chapter covers some of my contributions to secure computation through the introduction and construction of pseudorandom correlation generators (PCG), a cryptographic primitive that enables considerable efficiency improvements for a wide variety of secure computation protocols. I provide a step-by-step introduction to the notion of PCG and its security properties, outline the challenges in building them, and present a general framework for constructing PCGs. The chapter also contains extensive efficiency considerations and covers various optimizations, as well as extensions and generalizations of the notion of PCGs. Altogether, this provides a unified introduction to the work on pseudorandom correlation generators developed in my work over the past five years, aimed at a broad cryptography audience.<br/> <br/> Jury: <br/> Michel Abdalla, reviewer, DR CNRS at ENS Paris<br/> Benny Applebaum, reviewer, professor at Tel-Aviv University<br/> Ivan Damgård, examiner, professor at Aarhus University<br/> Carmit Hazay, reviewer, professor at Bar-Ilan University<br/> Sophie Laplante, examiner, professor at Université Paris-Cité </div> </div> </div> </div> <div class="level4"> <p> <br/> </p> </div> <h4 id="year_2023">Year 2023</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2023" id="plugin_include__en__seminaires__hdr__hdr2023"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Monday December 4, 2023, 2PM, Amphithéâtre Pierre-Gilles de Gennes du bâtiment Condorcet<br/> <strong>Sylvain Perifel</strong> (IRIF) <em>L'aléatoire par le prisme des polynômes et de la compression</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3544"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3544"><div class="bs-wrap bs-wrap-well well well-sm"> Jury :<br/> - Claire Mathieu, présidente, directrice de recherche au CNRS, Académie des sciences<br/> - Meena Mahajan, rapporteuse, professeure à l'Institut des sciences mathématiques de Chennai<br/> - Santiago Figueira, rapporteur, professeur à l'université de Buenos Aires<br/> - Olivier Bournez, rapporteur, professeur à l'École polytechnique<br/> - Damiano Mazza, examinateur, directeur de recherche au CNRS<br/> - Olivier Carton, examinateur, professeur à l'université Paris Cité, IUF<br/> <br/> « Résumé opérationnel » :<br/> Dans une première partie, nous comparerons quelques méthodes efficaces de compression (automates à pile, LZ'78, espace polylogarithmique), puis nous étudierons la « catastrophe du premier bit » pour l'algorithme de Lempel-Ziv, où l'ajout d'un seul bit peut changer le taux de compression. La seconde partie traitera de complexité algébrique, en particulier de bornes inférieures pour certains modèles de calcul de polynômes, et du célèbre problème de test d'identité polynomiale qui résiste encore aux tentatives de dérandomisation. </div> </div> </div> </div> <div class="level4"> <p> <br/> </p> </div> <h4 id="year_2022">Year 2022</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2022" id="plugin_include__en__seminaires__hdr__hdr2022"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Thursday December 15, 2022, 2PM, Amphithéâtre Pierre-Gilles de Gennes, Bâtiment Condorcet<br/> <strong>Arnaud Sangnier</strong> (IRIF, Université Paris Cité) <em>Algorithmic techniques for the verification of counter systems and parameterised networks</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3545"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3545"><div class="bs-wrap bs-wrap-well well well-sm"> Jury: <pre class="code"> Nathalie Bertrand - Examinatrice Christel Baier - Rapporteuse Véronique Bruyère - Examinatrice Thomas Colcombet - Examinateur Javier Esparza - Rapporteur Jérôme Leroux - Rapporteur</pre> <p> Résumé: Model-checking is a verification technique which is in the past has been successfully applied to verify automatically the behavior of finite state systems. This approach consists in modelling a computing system by a mathematical model, in translating its specification into a logical formalism and then in proposing algorithms to check whether a model satisfies a logical formula. When the considered models have an infinite number of states, this method can easily lead to undecidable model-checking problems and one has hence to find the right trade-off between the expressiveness of models and specification languages and the feasibility of the verification. In this thesis, I present my contributions to the field of verification of infinite states systems where I have considered two main families of models. The first one are counter systems which can be seen as programs manipulating variables (called counters) taking their value in the natural. The second one are parameterised networks which can be seen as an abstraction of distributed networks where the number of participating entities is not fixed a priori and is unbounded. For these different models, I study exhaustively when the automatic verification is feasible and in the positive cases I try to design model-checking algorithms with optimal complexity bounds. </p> <p> Plus d'informations disponibles sur la page web suivante : </p> <p> <a href="https://www.irif.fr/~sangnier/hdr.html" class="urlextern" title="https://www.irif.fr/~sangnier/hdr.html" rel="ugc nofollow">https://www.irif.fr/~sangnier/hdr.html</a> </div> </p> </div> </div> </div> <div class="level4"> <p> <br/> </p> </div> <h4 id="year_2021">Year 2021</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2021" id="plugin_include__en__seminaires__hdr__hdr2021"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Tuesday April 6, 2021, 2PM, Online<br/> <strong>Wolfgang Steiner</strong> (IRIF) <em>Numeration systems: automata, combinatorics, dynamical systems, number theory</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3546"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3546"><div class="bs-wrap bs-wrap-well well well-sm"> Composition du jury :<br/> Valérie Berthé, DR CNRS, Université de Paris, examinatrice<br/> Yann Bugeaud, Professeur, Université de Strasbourg, rapporteur<br/> Olivier Carton, Professeur, Université de Paris, président du jury<br/> Karma Dajani, Professeure, Universiteit Utrecht, rapporteuse<br/> Jean-Michel Muller, DR CNRS, ENS Lyon, examinateur<br/> Cyril Nicaud, Professeur, Université Gustave Eiffel, examinateur<br/> Jeffrey O. Shallit, Professeur, University of Waterloo, rapporteur<br/> Brigitte Vallée, DR CNRS émérite, Université de Caen Normandie, examinatrice<br/> <br/> Le manuscrit est disponible à l’adresse <a href="https://www.irif.fr/~steiner/hdr.pdf" class="urlextern" title="https://www.irif.fr/~steiner/hdr.pdf" rel="ugc nofollow">https://www.irif.fr/~steiner/hdr.pdf</a><br/> Les transparents sont disponibles à l'adresse <a href="https://www.irif.fr/~steiner/hdr_talk.pdf" class="urlextern" title="https://www.irif.fr/~steiner/hdr_talk.pdf" rel="ugc nofollow">https://www.irif.fr/~steiner/hdr_talk.pdf</a><br/> La soutenance sera diffusée à l'adresse <a href="https://www.youtube.com/channel/UCHbdRBy9VwdfYmBjl_ZIyeQ" class="urlextern" title="https://www.youtube.com/channel/UCHbdRBy9VwdfYmBjl_ZIyeQ" rel="ugc nofollow">https://www.youtube.com/channel/UCHbdRBy9VwdfYmBjl_ZIyeQ</a> </div> </div> </div> </div> <div class="level4"> <p> <br/> </p> </div> <h4 id="year_2019">Year 2019</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2019" id="plugin_include__en__seminaires__hdr__hdr2019"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Thursday November 28, 2019, 2PM, 3052<br/> <strong>Constantin Enea</strong> <em>Specifying and Verifying Consistency Properties</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3547"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3547"><div class="bs-wrap bs-wrap-well well well-sm"> Jury: <ol class=" fix-media-list-overlap"> <li class="level1"><div class="li"> Parosh Aziz Abdulla, Uppsala University, Sweden (examiner)</div> </li> <li class="level1"><div class="li"> Hagit Attiya, Technion, Israel (examiner)</div> </li> <li class="level1"><div class="li"> Ahmed Bouajjani (examiner)</div> </li> <li class="level1"><div class="li"> Giuseppe Castagna (reviewer)</div> </li> <li class="level1"><div class="li"> Suresh Jagannathan, Purdue University, United States (reviewer)</div> </li> <li class="level1"><div class="li"> Rupak Majumdar, Max Planck Institute Kaiserslautern, Germany (reviewer)</div> </li> <li class="level1"><div class="li"> Mooly Sagiv, Tel-Aviv University, Israel (examiner)</div> </li> </ol> <p> </div> </p> </div> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Friday November 22, 2019, 2PM, Amphi 6C, Halle aux Farines<br/> <strong>Yann Régis-Gianas</strong> (IRIF) <em>Quelques métamorphoses de programmes</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3548"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3548"><div class="bs-wrap bs-wrap-well well well-sm"> Jury:<br/> - Sandrine Blazy (examinatrice)<br/> - Giuseppe Castagna (rapporteur)<br/> - Roberto di Cosmo (examinateur)<br/> - Xavier Leroy (examinateur)<br/> - Peter Thiemann (rapporteur)<br/> - Stephanie Weirich (rapporteure) </div> </div> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Tuesday June 18, 2019, 10AM, Salle des Thèses, Halle aux Farines<br/> <strong>Yves Guiraud</strong> <em>Méthodes de réécriture en algèbre supérieure</em> <br/> </p> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Thursday May 16, 2019, 2PM, Salle 0011, Bâtiment Sophie Germain<br/> <strong>Pierre Charbit</strong> (IRIF) <em>About Some Hereditary Classes of Graphs : Algorithms - Structure - Coloration</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3549"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3549"><div class="bs-wrap bs-wrap-well well well-sm"> Rapporteurs:<br/> Laurent Viennot, Directeur de recherche, INRIA, Paris<br/> Alex Scott, Professeur, Oxford University<br/> Christophe Paul, Directeur de Recherche, CNRS, Montpellier<br/> <p> <br/> Jury:<br/> Pierre Fraigniaud, Directeur de Recherche, CNRS, Paris<br/> Frédéric Havet, Directeur de Recherche, CNRS, Sophia Antopolis<br/> Claire Mathieu, Directrice de Recherche, CNRS, Paris<br/> Christophe Paul, Directeur de Recherche, CNRS, Montpellier<br/> Alex Scott, Professeur, Oxford University<br/> Jean-Sébastien Sereni, Directeur de Recherche, CNRS, Strasbourg<br/> Laurent Viennot, Directeur de recherche, INRIA, Paris </div> </p> </div> </div> </div> <div class="level4"> <p> <br/> </p> </div> <h4 id="year_2018">Year 2018</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2018" id="plugin_include__en__seminaires__hdr__hdr2018"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Wednesday November 28, 2018, 2PM, Salle 2014 du Bâtiment Sophie Germain<br/> <strong>Enrica Duchi</strong> (IRIF) <em>Polyominoes, permutominoes and permutations</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3550"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3550"><div class="bs-wrap bs-wrap-well well well-sm"> La soutenance aura lieu devant le jury suivant : <ol class=" fix-media-list-overlap"> <li class="level1"><div class="li"> Frédérique Bassino, (LIPN, Université Paris 13)</div> </li> <li class="level1"><div class="li"> François Bergeron, (UQAM, Université du Québec à Montreal)</div> </li> <li class="level1"><div class="li"> Jean-Marc Fédou, (I3S, Université de Nice Sophia-Antipolis)</div> </li> <li class="level1"><div class="li"> Vlady Ravelomanana, (IRIF, Université Paris Diderot)</div> </li> <li class="level1"><div class="li"> Bruno Salvy, (LIP, ENS Lyon)</div> </li> <li class="level1"><div class="li"> Michèle Soria, (LIP6, Université Paris 6)</div> </li> </ol> <p> après avis des rapporteuses : </p> <ol class=" fix-media-list-overlap"> <li class="level1"><div class="li"> Marilena Barnabei, (Dipartimento di Matematica, Università di Bologna)</div> </li> <li class="level1"><div class="li"> Frédérique Bassino, (LIPN, Université Paris 13)</div> </li> <li class="level1"><div class="li"> Valérie Berthé, (IRIF, Université Paris Diderot)</div> </li> </ol> <p> </div> </p> </div> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Friday November 23, 2018, 2PM, Salle 234C, Halle aux Farines<br/> <strong>Christine Tasson</strong> (IRIF) <em>Sémantiques des Calculs Distribués, Différentiels et Probabilistes</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3551"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3551"><div class="bs-wrap bs-wrap-well well well-sm"> Depuis les années 60, la sémantique s'est avérée très utile pour introduire des langages de haut niveau permettant d'écrire des programmes complexes et de les comprendre à un niveau mathématique précis. Dans les années 80, la logique linéaire a été introduite par Girard, reflétant des propriétés sémantiques liées à l'utilisation des ressources. Cette direction a été poursuivie par Ehrhard dans les années 2000 avec l'introduction du lambda-calcul différentiel. Dans ces modèles, les programmes sont approximés par des polynômes, dont les monômes représentent les appels d'un programme à ses entrées lors de son exécution. Cette approche analytique a constitué un outil crucial pour l'étude des propriétés quantitatives apparaissant dans les langages de programmation probabiliste. En parallèle, depuis les années 90, plusieurs modèles géométriques ont été développés pour représenter des traces d'exécution dans les systèmes distribués. Dans cette thèse d'habilitation, nous présentons des modèles que nous avons étudiés dans ces trois domaines : les systèmes distribués, le lambda-calcul différentiel, la programmation probabiliste, ainsi que les techniques générales nécessaires et les résultats qu'ils nous ont permis d'obtenir. Celles-ci ont nécessité l'utilisation et le développement d'outils issus de la combinatoire, de la topologie dirigée, de l'analyse fonctionnelle, de la théorie des catégories et des probabilités. </div> </div> <p> Le jury est composé des membres suivants: Lisbeth Fajstrup (examinatrice), Marcelo Fiore (rapporteur), Pierre Fraigniaud (rapporteur), Achim Jung (examinateur), Alexandra Silva (examinatrice), Tarmo Uustalu (examinateur) </p> </div> </div> <div class="level4"> <p> <br/> </p> </div> <h4 id="year_2017">Year 2017</h4> <div class="level4"> </div> <div class="plugin_include_content plugin_include__en:seminaires:hdr:hdr2017" id="plugin_include__en__seminaires__hdr__hdr2017"> <div class="level4"> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Monday November 27, 2017, 2PM, Salle des Thèses, Halle aux Farines<br/> <strong>Stefano Zacchiroli</strong> (IRIF) <em>Large-scale Modeling, Analysis, and Preservation of Free and Open Source Software</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3552"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3552"><div class="bs-wrap bs-wrap-well well well-sm"> <a href="https://upsilon.cc/~zack/research/hdr/" class="urlextern" title="https://upsilon.cc/~zack/research/hdr/" rel="ugc nofollow">https://upsilon.cc/~zack/research/hdr/</a> </div> </div> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Monday November 20, 2017, 10AM, Salle 227C, Halle aux Farines<br/> <strong>Paul-André Melliès</strong> (IRIF) <em>Une étude micrologique de la négation</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3553"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3553"><div class="bs-wrap bs-wrap-well well well-sm"> La logique tensorielle est une logique primitive du tenseur et de la négation, dont l'objectif est de circonscrire les ingrédients élémentaires du raisonnement logique, et de les étudier au moyen des outils de l'algèbre contemporaine. <p> La logique est aussi conçue pour fonder la sémantique des jeux en théorie des types, et pour l'articuler de manière précise et harmonieuse avec la logique linéaire et la théorie des continuations dans les langages de programmation. </p> <p> <a href="https://www.irif.fr/~mellies/habilitation.html" class="urlextern" title="https://www.irif.fr/~mellies/habilitation.html" rel="ugc nofollow">https://www.irif.fr/~mellies/habilitation.html</a> </div> </p> </div> <p> <a href="https://www.irif.fr/en/seminaires/hdr/index" class="wikilink1" title="en:seminaires:hdr:index" data-wiki-id="en:seminaires:hdr:index">Habilitation defences</a><br/> Tuesday July 11, 2017, 2:30PM, Salle 0010, Bâtiment Sophie Germain<br/> <strong>Reza Naserasr</strong> (IRIF) <em>Projective Cubes, a coloring point of view</em> <span class="bs-wrap bs-wrap-button" data-btn-type="link" data-btn-size="xs" data-btn-collapse="b22-3554"><i class="dw-icons fa-lg fa fa-info-circle" style="color:#777" title=""></i></span><br/> </p> <div class="bs-wrap bs-wrap-collapse collapse" id="b22-3554"><div class="bs-wrap bs-wrap-well well well-sm"> The four-color theorem states that every simple planar graph admits a homomorphism to $K_4$. In many proposed extensions or reformulations of this theorem $K_4$ is regarded as the complete graph on four vertices. In this work we consider $K_4$ as the Cayley graph “$\mathbb Z_2^2, {01,10,11}$”. Main observation, which is hidden behind the fact that 2 is a very small number, is that {01,10} is a basis of $\mathbb Z_2^2$ and that 11=01+10. <p> The generalization of this view is the Cayley graph $\mathbb Z_2^k, {e_1,e_2, \cdots, e_k, J}$ which is isomorphic to the projective cube of dimension $k$ also known as the folded cube. </p> <p> Thus we consider the problem of mapping planar graphs into projective cubes, and show that this question is related to several other notions of coloring such as the edge-chromatic number of planar multi-graphs, circular chromatic number and the fractional chromatic number. </p> <p> Finally, after providing a test to decide if a graph $B$ of odd-girth $2k+1$ admits a homomorphism from any graph of tree-width at most $t$ and odd-girth at least $2k+1$, we show that every 3-tree of odd-girth at least $2k+1$ admits a homomorphism to the projective cube of dimension $2k$. </div> </p> </div> </div> </div> <div class="level4"> </div> </div></div><p> <style> .page a.urlextern, .page a.interwiki, .page a.windows, .page a.mail, .page a.media { padding-left: 0 !important; background: none !important; } .page { text-align: justify; } body {font-size: 15px; font-weight: 300; color: #333333; } b,strong {font-weight: 600; color: #333333; } p {margin-bottom:1.3em} h1 {font-size: 2.8em; margin-bottom:1.5em; font-weight: 400; } h2 {font-size: 2.2em; margin-bottom:1.2em; font-weight: 400; } h3 {font-size: 1.9em; margin-bottom:0.9em; font-weight: 400; } h4 {font-size: 1.7em; margin-bottom:0.8em; font-weight: 300; } h5 {font-size: 1.5em; margin-bottom:0.8em; font-weight: 300; } h5 {font-size: 1.4em; margin-bottom:0.8em; font-weight: 300; } </style> </p> </div> </div> <div class="small text-right"> </div> </article> </div> </main> <footer id="dw__footer" class="dw-container py-5 dokuwiki container-fluid">  <div class="dw-container small container-fluid mx-5"> <div class="footer-dw-title"> <div class="media"> <div class="media-left">  <img src="https://www.irif.fr/_media/logo_footer.png" alt="" class="media-object" style="height:10px" /> </div> <div class="media-body"> <div class="row"> <div class="col-sm-2"> <h4 class="media-heading"></h4> <p> </p> </div> <div class="col-sm-10"> </div> </div> </div> </div> </div> <a style="font-size:12px" href="https://www.irif.fr/informations/mentions-legales">Mentions légales</a> <div class="footer-license row"> <hr/> <div id="dw__license" class="col-sm-6"> </div> <div class="col-sm-6"> </div> </div> </div>  </footer> <a href="#dokuwiki__top" class="back-to-top hidden-print btn btn-default" title="skip to content" accesskey="t"> <span class="iconify" data-icon="mdi:chevron-up"></span> </a> <div id="screen__mode"> <span class="visible-xs-block"></span> <span class="visible-sm-block"></span> <span class="visible-md-block"></span> <span class="visible-lg-block"></span> </div> <img src="https://www.irif.fr/lib/exe/taskrunner.php?id=en%3Aseminaires%3Ahdr%3Aindex&1732751067" width="2" height="1" alt="" /> </div> </body> </html>