PRESENTATION | RESEARCH | TEACHING | CONFERENCES | DIFFUSION FRANÇAIS
moi
Baptiste Chantraine
Maître de conférences HDR,
Laboratoire de Mathématiques Jean Leray,
2 rue de la Houssinière,
BP 92208 ,
F-44322 Nantes Cedex 3,
France.
Office: 132
Phone: +33 2 51 12 59 30
Email: firstname.lastname@univ-nantes.fr
(and my pgp public key).
 
RESEARCH
Interêts de recherche:

I am interested in the algebraic invariants of Legendrian sub-manifolds of contact manifolds. Mostly, I study the Chekanov algebra whose homology yields Legendrian contact homology and the invariants one can extracts from it. I am also interested in the correspondence between these invariants and those coming from generating families and constructible sheaves.

Geometrically, the functoriality of these invariants is seen via Lagrangian cobordisms. In low dimension, adjunction inequality leads to some applications of this relation to knot theory. In higher dimensions, studying twisted coefficients one can prove that some of those cobordisms are trvial using the h-cobordism theorem.

My work is summarized in my memoir of "habilitation à diriger la recherche" (defended December 10th 2019 , slides).

Various projects and services:

I co-organise the Topology Geometry and Algebra seminar in Nantes

I am also a member of the ANR project ENUMGEOM studying enumerative aspects of symplectic and real geometry and of the project COSYDY studying conformally symplectic dynamics.

Publications and prepublications:

  • (with Kevin Sackel) Products of locally conformal symplectic manifolds ,
    prepublication 2024 arXiv:2401.14918 .
  • (with Georgios Dimitroglou Rizell, Paolo Ghiggini et Roman Golovko) Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors,
    Annales Scientifiques de l'ENS, Fasc. 1 Tome 57 (2024); 10.24033/asens.2570.
  • (with Noémie Legout)Doubly slice knots and obstruction to Lagrangian concordance ,
    Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1605-1609; 10.5802/crmath.478.
  • Reeb chords of Lagrangian slices,Journal of Fixed Point Theory and Applications volume 24, Article number: 26 (2022), https://doi.org/10.1007/s11784-022-00940-1.
  • (with Georgios Dimitroglou Rizell, Paolo Ghiggini et Roman Golovko) Floer theory for Lagrangian cobordisms,
    ``Journal of differential geometry'' 114 (2020) no. 3;doi:10.4310/jdg/158337721
  • (with Emmy Murphy)Conformal symplectic geometry of cotangent bundles,
    ``Journal of symplectic geometry'' vol. 17 (2019) no. 3; doi:http://dx.doi.org/10.4310/JSG.2019.v17.n3.a2
  • (with Vincent Collin et Georgios Dimitroglou Rizell)Positive Legendrian isotopies and Floer Theory,
    ``Annales de l'institut Fourier, Volume 69 (2019) no. 4, p. 1679-1737''; DOI:10.5802/aif.3279
  • (with Lenhard Ng et Steven Sivek) Representations, sheaves, and Legendrian (2,m) torus links,
    ``Journal of the London Mathematical Society'' Voume 100 Issue 1; doi:10.1112/jlms.12204.
  • (with Georgios Dimitroglou Rizell, Paolo Ghiggini et Roman Golovko) Noncommutative augmentation categories ,
    Proceedings of Gökova Geometry-Topology Conference 2015, 116--150; ISBN-13 9781571463210.
  • Lagrangian concordance is not a symetric relation,,
    Quantum Topol. 6 (2015), no. 3, 451 474; DOI:10.4171/QT/68.
  • (with Georgios Dimitroglou Rizell, Paolo Ghiggini et Roman Golovko) Floer homology and Lagrangian concordance,
    Proceedings of Gökova Geometry-Topology Conference 2014, 76--113; ISBN-13 9781571463074.
  • Exact Lagrangian cobordisms with disconnected Legendrian ends,
    Proc. Amer. Math. Soc. 143 (2015), 1325-1331; doi: 10.1090/S0002-9939-2014-12302-1.
  • (with Frédéric Bourgeois) Bilinearised Legendrian contact homology and the augmentation category,
    Journal of Symplectic Geometry Volume 12 (2014) Number 3; doi: 10.4310/JSG.2014.v12.n3.a5.
  • Some non-collarable slices of Lagrangian surfaces,
    Bulletin of the London Mathematical Society (2012) Volume 44 Issue 5: 981-987; doi: 10.1112/blms/bds026.
  • Lagrangian concordance of Legendrian knots,
    Algebraic and Geometric Topology Volume 10 issue 1, 2010; doi: 10.2140/agt.2010.10.63.







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    TEACHING
    RESPONSABILITIES:

    I am in charge of the first year of the Master program "Mathématiques Fondamentales et Appliquées". Informations on this formation are here..
    To contact me about this program you can use the following adress Master1-MFA@univ-nantes.fr.

    2023-2024:

    On the first semestre I teach the Master 2 class "Introduction to Algebraic Topology", the master 1 class on Differential Geometry and supervise the group project on "Fundamental Group and covering spaces".

    Past:

    On the second semester 2020-2021 I gave the Master 2 class on "introduction to symplectic geometry".

    Classe notes and exercices are here:

    Chapter 1:Hamiltonian vector fields.
    Exercises sheet 1.
    Chapter 2:Symplectic linear algebra.
    Exercises sheet 2.
    Chapter 3:Symplectic manifolds.
    Exercises sheet 3.
    Chapter 4:Symplectic reduction.
    Chapter 5:Generating families.

    On the first semestre of 2019-2020 I gave a more elementary version of this class. You will find here scanned notes (in french) of the class and some exercices sheets.
    Chapter 0:Champs de vecteurs.
    Exercises sheet 1.
    Chapter 1:Champs de vecteurs hamiltoniens.
    Exercises sheet 2.
    Chapter 2:Algèbre linéaire symplectique.
    Exercises sheet 3.
    Chapter 3:Variétés symplectiques.
    Chapter 4:Réductions symplectiques.
    Exercises sheet 4.

    In 2016 I gave a mini class on contact geometry. Here are some scanned note (in french):
    Chapter 1:Examples.
    Chapter 2:Définition de base.
    Chapter 3:Quelques résultats de fléxibilité.
    Chapter 4:Structures de contact sur R^3.
    Chapter 5:Réduction.
    Chapter 6:Familles génératrices.
    Chapter 7:Cobordismes lagrangiens.

    In 2014, I gave an advanced class on Fukaya categories. Here are some very incomplete (and probably containing mistakes) notes:
    Introduction to Fukaya categories.




     
     
    CONFERENCES
    Some videos of talks:
  • On Lagrangian intersections in locally conformally symplectique manifolds at AIM (online), march 2021.
  • On restrictions of the fundamental groups of some Lagrangian cobordisms at the IAS, February 2016.
  • On positive Legendrian isotopies and Floer theory in Banff, March 2016.
    • Conferences:
  • Séminaire de topologie et géométrie (Toulouse),,
    Structures produits en géométrie localement conformément symplectique , february 24th 2024
  • Geometry seminair (Brusells),,
    Product of lcs manifolds, January 15th 2024
  • Symplectic, real, and tropical aspects of enumerative geometry (Paris),,
    Rigidité en géométrie localement conformément symplectique., september 15th 2023
  • School on conformal symplectic dynamics and related fields (CIRM Marseille),,
    Conformal Dynamics on locally symplectic manifolds , may 8-9 2023
  • Séminaire de Géométrie et application (Strasbourg),,
    Rigidité en géométrie localement conformément symplectique. , april 3rd 2023
  • Séminaire de Géométrie et Topologie (Toulouse),,
    Sous-variétés Lagrangiennes compactes et représentations de l'algèbre de Chekanov-Eliashberg. , november 8th 2022
  • Séminaire de Systèmes dynamiques, Analyse et Géométrie (Avignon),,
    Sous-variétés Lagrangiennes compactes et représentations de l’algèbre de Chekanov-Eliashberg., october 18th 2022
  • Séminaire Nantes-Orsay de géométrie symplectique et de contact (Nantes),,
    Rigidité en géométrie localement conformément symplectique, may 20th 2022
  • Séminaire de topologie (Grenoble),,
    Objets compacts de la catégorie de Fukaya et algèbre de Chekanov, January 14th 2022
  • Séminaire de géométries (Lyon),,
    Objets compacts de la catégorie de Fukaya et algèbre de Chekanov, December 10th 2021
  • Séminaire de géométrie différentielle (Nancy), online,
    Topologie des sous-variétés lagrangiennes et génération de la catégorie de Fukaya d'une variété de Weinstein, March 22nd 2021
  • AIM Workshop, En ligne,
    Lagragian intersecion in locally conformally symplectic manifolds, march 15th 2021.
  • Uppsala geometry and toplogy seminar, Online,
    Invariants of Legendrian submanifolds in non-coorientable contact structures., June 24th 2020.
  • Brussel-London geometry seminar, Online,
    Invariants of Legendrian submanifolds in non-coorientable contact structures., May 7th 2020.
  • Séminaire de Géométrie, Université de Lyon,
    Invariants des sous-variétés legendriennes dans les structures de contact non co-orientables., February 21st 2020.
  • Rencontre GENRE: Tropical Geometry in Europe, Université de Nantes,
    Invariants of Legendrian submanifolds in non co-orientable contact structure , January 22nd 2020.
  • Séminaire Topologie Géométrie et Algèbre, Université de Nantes,
    Représentations de l'algèbre de Chekanov des noeuds toriques (2,m) et identités matricielles, October 10th.
  • Summer school: Current Trends in Symplectic Topology, CRM Montreal,
    Augmentations: why do we need them and what are they good for?, July 1st 2019.
  • Conference: Homological Algebra, Microlocal Analysis and Symplectic Geometry, CRM Montréal,
    Applications of Floer theory for Lagrangian cobordisms,, June 24th 2019.
  • Séminaire LACIM, Université du Québec à Montréal,
    Généralisation de l'identité de Sylvester et noeuds legendriens,, May 17th 2019.
  • Columbia Symplectic Geometry, Gauge Theory, and Categorification Seminar, Columbia University,
    Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries,, April 26th 2019.
  • Geometry/Physics Seminar, Northwestern University,
    Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries,, March 7th 2019.
  • Séminaire symplectique, Université du Québec à Montréal,
    Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries,, March 1st and 22nds 2019.
  • Topology and related seminars, University of British Columbia,
    Lagrangian cocores generates the wrapped Fukaya category,, February 27 2019.
  • Séminaire CIRGET, Université du Québec à Montréal,
    Sous-variétés lagrangiennes des variétés de Weinstein,, January 11 2019.
  • Geometry and Topology Seminar , MIT,
    Twisted complexes and Floer theory for Lagrangian cobordisms,, November 26th 2018.
  • Colloquium, University of Ottawa,
    Lagrangian submanifolds of Weinstein manifolds, October 19th 2018.
  • Symplectic Seminar, CIRGET, Montreal,
    Categories associated to Legendrian links I et II, September 21st et October 26th 2018.
  • Geometric structures on 3 and 4 manifolds, IUC Dubrovnik,
    Categories associated to Legendrian links, June 11th 2018.
  • Séminaire de Géométrie Algébrique, Université d'Anger.
    Générateurs de la catégorie de Fukaya d'un secteur de Weinstein,, January 19th 2018.
  • Séminaire de Topologie Géométrie et Algèbre, Université de Nantes.
    Chirurgies lagrangiennes et complexe tordus en homologie de contact legendrienne, November 23rd 2017.
  • Séminaire de Géométrie et Topologie, Université de Toulouse.
    Intersections lagrangiennes dans les fibrés cotangents conformément symplectiques, November 14th 2017.
  • Colloque 2017 du GDR 2875, Topologie Algébrique et Applications, Université Paris Diderot
    Catégories associées à une sous-variété legendrienne, October 20th 2017.
  • Ottawa algebra seminar, University of Ottawa,
    Conformal symplectic geometry of cotangent bundles, June 13th 2017.
  • Séminaire Symplectix, Institut Henri Poincaré,
    Isotopies legendriennes positives et homologie de Floer, March 3rd 2017.
  • Séminaire Quimpériodique, Quimper.
    Obstructions à l'existence d'isotopies legendriennes positives, January 19th 2017.
  • Séminaire de Géométrie et Topologie, Université de Toulouse.
    Isotopies legendriennes positives et homologie de Floer, December 13th 2016.
  • MSI Workshop on Low-Dimensional Topology & Quantum Algebra,Australian National University, Canberra.
    Positive Legendrian isotopies and Floer theory, November 2nd 2016.
  • Séminaire de Géométrie,Université de Lyon I.
    Isotopies legendriennes positives et homologie de Floer, October 21st 2016.
  • Topology Seminar,University of Georgia, Athens.
    Restrictions on the topology of Lagrangian cobordisms, April 25th 2016.
  • Geometry/topology Seminar,Duke University.
    Positive Legendrian isotopies and Floer theory , Apris 6th 2016.
  • Interactions of Gauge Theory with Contact and Symplectic Topology in Dimensions 3 and 4 ,BIRS, Banff.
    Positive Legendrian isotopies and Floer theory , March 22nd 2016.
  • Geometry and Topology Seminar,MIT, Cambridge.
    Non commutative augmentation category , March 7th 2016.
  • Augmentations and Legendrians at the Institute for Advanced Study,IAS, Princeton.
    Restrictions on the fundamental group of some Lagrangian cobordisms. , Febraury 11th 2016.
  • Columbia Symplectic Geometry, Gauge Theory, and Categorification Seminar,Columbia University, New York.
    Legendrian contact homology and positive isotopies , February 5th 2016.
  • Flexibility and contact geometry,Université libre de Bruxelles
    Legendrian contact homology and positive isotopies , December 16th 2015.
  • Geometry and Topology Seminar,University of Glasgow
    Legendrian contact homology and positive isotopies , November 9th 2015.
  • Symplectic Geometry Seminar,Institut Mittag-Leffler, Stockholm
    Legendrian contact homology and positive isotopies , October 13th 2015.
  • Séminaire CIRGET,UQAM Montréal
    Legendrian contact homology and positive isotopies , August 28th 2015.
  • Recent challenges in contact geometry,CIRM, Marseille
    Positive Legendrian isotopy and Floer theory, June 12th 2015.
  • Séminaire de géométrie et systèmes dynamiques,Université de Bourgogne
    Sur la topologie de endocobordisme lagrangiens, May 21st 2015.
  • Seminar on symplectic and contact geometry,Cologne University
    On the topology of Lagrangian endocobordisms, March 27th 2015.
  • Séminaire de Théorie spectrale et géométrie, Université de Grenoble,
    Sur la topologie des endocobordismes lagrangiens, March 12th 2015.
  • Séminaire de géométrie et topologie, Université de Toulouse,
    Sur la topologie des endocobordismes lagrangiens, March 3rd 2015.
  • Séminaire de géométrie et application, Université de Strasbourg,
    Sur la topologie des endocobordismes lagrangiens, February 16th 2015.
  • The Philadelphia Area Contact / Topology Seminar, Bryn-Mawr,
    Floer thoery for Lagrangian cobordisms and topology of Lagrangian endocobordisms, December 16th 2014.
  • Rigidity and Flexibility in Symplectic Topology and Dynamics, Lorentz center Leiden,
    Floer thoery for Lagrangian cobordisms and topology of Lagrangian endocobordisms, 2014 July 23rd.
  • Gokova Geometry/Topology conference, Gokova,
    Floer theory for Lagrangian cobordisms-2: applications., 2014 May 29th.
  • Symplectic Geometry Seminar, ETH Zurich,
    On the topology of Lagrangian cobordisms between Legendrian submanifolds, 2014 March 17th.
  • CIRGET Seminar, UQAM,
    Floer Theory for Lagrangian cobordisms., 2014 February 21st.
  • Geometry and Topology Seminar, MIT,
    Floer Theory for Lagrangian cobordisms., 2014 February 18th.
  • KCL Geometry Seminar, King's College London,
    Lagrangian Floer Theory for Lagrangian cobordisms., 2013 December 10th.
  • Séminaire Symplectix, Institut Henri Poincaré,
    Lagrangian Floer Theory for Lagrangian cobordisms., 2013 November 8th.
  • Séminaire Géométrie Topologie Dynamique, Université Paris 11,
    Théorie de Floer pour les cobordismes lagrangiens., 2013 September 26th.
  • Séminaire de géométrie et dynamique , ENS Lyon,
    Homologie de contact legendrienne bilinéarisée et catégorie d'augmentation., 2013 September 18th.
  • Séminaire de Topologie Géométrie et Algèbre , Université de Nantes,
    Théorie de Floer pour les cobordismes lagrangiens., 2013 April 11th.
  • Séminaire Bruxelles-Cologne , Université Libre de Bruxelles,
    Bilinearised Legendrian contact homology and obstructions to Lagrangian concordances., 2013 March 1st.
  • Séminaire de géométrie , Université de Toulouse,
    Homologie de contact bilinéarisée et obstruction à l'existence de concordances lagrangiennes., 2013 February 26th.
  • Séminaire de géométrie algébrique , Université d'Angers,
    Sur la non-symétrie de concordances lagrangiennes, 2012 December 14th.
  • Journée des nouveaux mathématiciens recrutés dans la région des Pays de la Loire, Université de Nantes,
    Constructions de cobordismes Lagrangiens et tranches non-colliésables de surfaces Lagrangiennes., 2012 September 28th.
  • Séminaire Symplectix, Institut Henri Poincaré,
    Homologie de contact legendrienne bilinéarisée., 2012 March 9th.
  • Geometry and Topology seminar, Uppsala University,
    Bilinearised Legendrian contact homology, 2011 November 16th.
  • Les colloques du Mardi, Institut de Mathématiques, Université de Neuchatel,
    Example of non-collarable slices of Lagrangian surfaces, 2011 October 25th.
  • Séminaire de dynamique et géométrie, Institut de Mathématiques, Université de Neuchatel,
    Bilinearised Legendrian contact homology, 2011 October 25th.
  • FNRS contact group, Université Libre de Bruxelles,
    Constructions of Lagrangian cobordisms and non-collarable slices of Lagrangian surfaces, 2011 September 12th.
  • Differential Geometry Seminar, University of Cambridge,
    Lagrangian cobordisms of Legendrian knots and applications, 2011 March 2nd.
  • Séminaire de Topologie, Géomètrie et Algèbre, Laboratoire Jean Leray, Université de Nantes,
    Cobordismes lagrangiens de nœuds legendriens, 2009 November 5th.
  • Workshop on Symplectic Geometry, Contact Geometry, and Interactions, IRMA Université de Strasbourg,
    Non-symmetry of Lagrangian concordances, 2009 January 31st.
  • Symplectic Geometry Seminar, Leipzig Universität,
    Non-symmetry of Lagrangian concordances, 2008 October 10th.
  • Seminar on symplectic and contact geometry, Université Libre de Bruxelles,
    Sur la non-symétrie de concordances lagrangiennes, 2008 April 30th.
  • Séminaire Symplect'X, Centre de Mathématiques Laurent Schwartz (Ecole Polytechnique Paris),
    Cobordismes lagrangiens entre nœuds legendriens, 2008 January 11th.
  • Seminar on symplectic and contact geometry, Unversité libre de Bruxelles,
    Lagrangian cobordism of Legendrian knots, 2007 October 15th.
  • Interaction of geometry and topology in low dimension, Banff Internationnal Research Station,
    Cobordisms of Legendrian knots, 2007 March 26th.
  • Séminaire de topologie symplectique, Université de Montréal,
    Concordances lagrangiennes, 2006 February 7th.
  • Topics on 3 Manifolds, Centre Interuniversitaire de Recherche en Géométrie Et Topologie (UQAM),
    Concordances lagrangiennes des nœuds legendriens, 2005 May 16th.






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    DIFFUSION AND MEDIATION.
    Communication
    I am "chargé de mission de communication" for the faculty of science.
    Arts and sciences

    I am co-coordinator of the activities around Arts and Science in the Laboratoire Jean Leray. Most of the informations on our actions are on the website of the Maison des Mathématiques de l'Ouest.

    During the year 2022-2023, I collaborate on the scientific part of the project "La terre est bleu comme un orange" de Katerini Antonakaki. We supervised some workshop in the School Jules Simon in Saint-Nazaire et the project was presented in laboratoire Jean Leray and in Athenor .

    During the second semesters of the year 2020-2021 and 2021-2022 I supervised a discovery teaching on digital art and sciences with the artist MAOTIK . During the second class the students worked on creating a numerical tree generated by meteoroligicalk data, here is a demo video

    This is in collaboration with Stereolux and we work on the software TOUCHDESIGNER .

    These workshops lead to restitutions by the students in April.

    With MAOTIK we gave a conference on relations between and arts and sciences in Stereolux during the "nuit blanche des chercheurs 2021" in Nantes.

    5 minutes Lebesgue.

    I am the local organiser in Nantes of the 5 minutes Lebesgue , some series of 5 minutes talks on mathematics for a various audience (unfortunately on break at the moment).

    Large audience talks.

  • A five minutes large audience talk on local Gauss-Bonnet formula on the sphere in Nantes, March 2017.
  • One for a more advanced audience on torsion in the fundamental group in Nantes, March 2018.
  • Here are some slides on talks that I gave in CEGEP Saint-Laurent et in Outaouais in Québec in 2019 (animations does not work on all pdf readers ...).

    • MATHh.en.JEANS

    I supervised several workshops MATHh.en.JEANS

    BSSM

    I gave two lectures in "Brussels Summer School of Mathematics" in 2010 and en 2011

    These lectures lead to lecture notes in the books here and there