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  • Post-doc positions
    Oct 4, 2017 to Dec 1, 2017
    lebesgue_money.png Henri Lebesgue Center offers post-doc positions for researchers in mathematics.

    Description

    The Lebesgue Center and its partners, Région Bretagne & Région Pays de la Loire (DéfiMaths project), are opening applications for three post-doctoral positions in mathematics for a period of 2*12 months. The hired applicant will conduct his/her research at one of these Insitutes:

    Irmar of Rennes
    LMJL of Nantes
    LMBA of Brest and Vannes
    LAREMA of Angers

    The positions are open to all research areas present within the four Institutes. They do not include an obligation to teach.

    The net salary will be 2 100 Euros per month.

    Deadlines

    The application is open.

    Sending application: between the 4th of October 2017 and the 1st of December 2017.

    The positions are expected to begin on September 1st or October 1st, 2018.

    Eligibility

    Candidates must have completed a PhD in mathematics, or equivalent, at the date of taking office. The candidate must submit an original research project including a collaboration with one or more local researcher (s) of Irmar, LMJL,LMBA, or LAREMA.

    Applicants must complete the online form where they have to join the following documents:

    • CV describing the candidate's profile and professional experience (list of publications, research topics, activities)
    • Cover letter including the research project
    • At least two letters of recommendation, including one from the local researcher involved in the project

    For more information, please contact us at post-doctorant[at]lebesgue.fr.

    Selection

    The selection is carried by the Lebesgue Scientific Committee.

    Nominees

    2017-2018
    2016-2017
    2015-2016
    2014-2015
    2013-2014

  • Lebesgue Master Scholarship
    Nov 15, 2017 to Mar 15, 2018
    lebesgue_money.png The Lebesgue Center offers 10,000€ scholarships to outstanding mathematics students applying for a master programme in mathematics, for a fist year of Master (M1) or for a second year of Master (M2), in Rennes, Nantes, Angers, Brest or Vannes.

    Eligibility

    The stipend is 10,000 euros per year.

    The M1 scholarships are open to all students who have completed a bachelor's degree in mathematics (or related) at the end of the academic year 2016-2017. The applicants for the Lebesgue M1 scholarship should certify a B1 level of proficiency of the French language.
    A student applying for the first year of a master (M1) will be allowed to apply for another scholarship for the second year (M2).

    The M2 scholarships are open to all students who have completed the first year of a master in mathematics (or related) at the end of the academic year 2016-2017.
    The courses of the second year of Master (M2) may be taught in English.

    The application of the Lebesgue scholarship is independent from the application to Masters programmes, whom modalities are indicated in the dedicated websites.

    Deadlines

    The application for the lebesgue Master Scholarship is open until March 15th, 2018.
    The results of the selection process will be edited in April 2017.

    Contact

    Applicants can obtain more information about the masters programmes on the page: Information.

    Application

    Applicants must complete the online form and attach the documents:
    - CV
    - Transcripts
    - Cover letter
    - One or more letters of recommendation.

    Applicants must submit the application only when it is complete. Only electronic submission using the online form will be considered.

    Selection

    The selection will be carried out by the Lebesgue Scientific Committee and the heads of the Masters programmes. It will be based on the academic quality of the applicant.

  • Mathematic world
    Nov 23, 2017

    Présentation

    Le séminaire, de fréquence trimestrielle, s'adresse en priorité aux étudiants de licence. Les exposés de 45 minutes sur des sujets variés seront suivis d'un repas convivial.

    12:30 → 13:15 : exposé et questions
    13:15 → 14:00 : repas et discussions

    Lieu

    Le séminaire a lieu à l'Irmar, bâtiment 22-23, rez-de-chaussée, salle 004-006.

    Prochain exposé

    Intervenant: François Maucourant

    Sujet: Les nombres p-adiques

    En 1897, Kurt Hensel a introduit une nouvelle classe de nombre, les nombres "p-adiques", qui sont désormais des acteurs majeurs en théorie des nombres. On expliquera comment les écrire, calculer avec, et quelques applications.

    Date: Jeudi 23 novembre 2017

    Inscription

    Les inscriptions en ligne sont ouvertes jusqu'au dimanche 19 novembre 2017.

  • Colloquium de mathématiques de Rennes
    Nov 27, 2017

    Dans la suite, le colloquium de mathématiques de Rennes reprend le lundi 27 novembre à 16h30 en salle 04-06 du rez-de chaussée du bâtiment 22, sur le Campus de Beaulieu.

    A l'honneur cette fois-ci Irène Waldspurger (CNRS-CEREMADE, Paris Dauphine) qui abordera les "Problèmes de reconstruction de phase". Plus d'information ici

  • School - Masterclass 2017
    Dec 19, 2017 to Dec 21, 2017

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    Angers, from December 19th to December 21st

    Organization board: Etienne Mann

    We organize a masterclass in Angers, from 19th to 21st of December, 2017. Lectures will be in the morning sessions. We will have two parallel sessions:

    • Etienne Mann : Introduction to algebraic stacks
      We will introduce the notion of fibered category, Grothendieck topology and stacks. We will illustrate these notions on simple examples. These lectures are for Master (or PhD) students who had followed a introduction to algebraic geometry that is algebraic varieties and sheaves.
    • Loic Chaumont: Application of the matrix-tree-theorem

    The organisation board will pay the housing with breakfast and the lunches. The dinners are not payed by the organizers. For the travel expenses, we will do our best in the limit of our budget.

    Deadline 15th novembre. Limit 30 participants maximum.

  • Workshop - Numerical methods for algebraic curves
    Feb 19, 2018 to Feb 23, 2018

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    Rennes, from February 19th to February 23rd

    Organization board: Xavier Caruso, David Lubicz, Christophe Ritzenthaler, Marie-Françoise Roy

    This workshop will bring together researchers in complex and real algebraic geometry and applied mathematics (physics and cryptography) to discuss numerical methods and open problems on algebraic curves. There will be a number of introductory talks to each of the following topics and invited lectures from specialists: - Theoretical physics/DPE - Computations with the Jacobian - Random real topology - Complexity of computing topology of real algebraic curves - p-adic methods and applications to cryptography

  • Conference - Mathematics and Enterprises Days
    Apr 12, 2018 to Apr 13, 2018

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    Vannes, from April 12th to April 13th

    Organization board: Christophe Berthon, Eric Darrigrand, Emmanuel Frénod, Fabrice Mahé, Loïc Chaumont

    Pour répondre aux besoins croissants en moyens de calcul, les entreprises et les laboratoires de recherche développent intensément de nouvelles méthodes numériques, des logiciels et du matériel. L'objectif de ces journées est de permettre aux différents acteurs d'échanger sur les dernières avancées pour améliorer les performances du calcul scientifique. Des exemples d'applications seront présentés dans plusieurs domaines : auto-apprentissage, consommations électriques, télédétection, biologie...
    Ces journées sont organisées par l’agence Lebesgue de mathématiques pour l'innovation dont une des missions est de promouvoir les relations entre les mathématiciens et les scientifiques des entreprises.
    L’Agence est un interlocuteur naturel pour tout acteur du monde industriel confronté à un problème mathématique identifié. Il s’agit d’offrir les meilleures compétences mathématiques disponibles dans les Unités Mixtes de Recherche en Bretagne et Pays de la Loire, en particulier dans le domaine du calcul scientifique.

  • School - Fundamentals and practice of finite elements
    Apr 16, 2018 to Apr 20, 2018

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    Roscoff, from April 16th to April 20th

    Organization board: Martin Costabel, Eric Darrigrand, Monique Dauge, Yvon Lafranche

    Scientific board: Monique Dauge (Univ. Rennes 1), Ilaria Perugia (TU Wien)

    This school will combine high-level courses on theoretical aspects of finite elements, with more practical implementation issues via an open source C++ library . We propose three different activities:

    1) The three main courses (ca 5h each) given by

    Ricardo Nochetto, University of Maryland, USA
    Adaptive Finite Element Methods: Convergence and Optimality

    Paul Houston, University of Nottingham, UK
    Discontinuous Galerkin Finite Element Methods on Polytopic Meshes

    Ralf Hiptmair, ETH Zürich, Suisse
    Boundary Element Methods: Design, Analysis, and Implementation

    2) An initiation to the finite element library XLiFE++ by Eric Lunéville, POEMS team, ENSTA ParisTech, followed by several practical sessions on computers.

    3) A few mini-courses about different related questions (eigenvalues, integral equations, fast methods, singularities) given by members of the organization board.

Conference - Loop spaces in geometry and topology

Titres et résumés

Mohammed Abouzaid

Title: Symplectic cohomology and loop homology

Abstract: The string topology of Chas-Sullivan produces operations on the homology of the free loop space of orientable manifolds, and analogous structures are known to exist on the symplectic cohomology of their cotangent bundles. Work of Kragh has indicated that these groups are only isomorphic under the assumption that the manifold is Spin. The goal of this minicourse is to define twisted versions of loop space homology and symplectic cohomology for an arbitrary closed smooth manifold which are isomorphic to each other. I will also explain how to build Batalin Vilkovisky structures on the two sides which are isomorphic. Reference: http://arxiv.org/abs/1312.3354

Denis Auroux

Title: A plethora of Lagrangian tori

Abstract: Over the last decade, Lagrangian Floer homology and Fukaya categories have led to significant progress in our understanding of Lagrangian submanifolds, especially in cotangent bundles. And yet, recent results suggest that even the simplest symplectic manifolds contain plenty of "exotic" Lagrangian tori, and the classification up to Hamiltonian isotopy remains quite mysterious. We will review various examples (some of which have appeared in Renato Vianna's thesis).

Somnath Basu

Title: The closed geodesic problem for four manifolds

Abstract: We will explain why a generic metric on a smooth four manifolds (with second Betti number at least three) has the exponential growth property, i.e., the number of geometrically distinct periodic geodesics of length at most l grow exponentially as a function of l. Time permitting, we shall explain related topological consequences.

Alexander Berglund

Title: Loop spaces and Koszul algebras

Abstract: I will begin by briefly reviewing Koszul duality for algebras over operads and discuss the relation between Koszulness and formality. Then I will explain how Koszul algebras can be used to construct tractable algebraic models for computing the homology of free and iterated loop spaces.

Ralph Cohen

Title: Calabi-Yau categories, string topology, and the Floer field theory of the cotangent bundle.

Abstract: I will describe joint work with Sheel Ganatra, in which we prove an equivalence between two chain complex valued topological field theories: the String Topology of a manifold M, and the Floer field theory of its cotangent bundle. This expands upon results of Viterbo, Abbondandolo and Schwarz, Abouzaid, and others. We use recent work of Kontsevich and Vlassopolous which describes two duality conditions among A-\infty-algebras and categories and show how they give rise to topological field theories. These "Calabi-Yau" conditions are related to the two dimensional cobordism hypothesis viewpoint of Lurie. We use this perspective to prove the equivalence of the theories above. We then show how Koszul duality affects the Calabi-Yau condition, and how it gives rise to a duality relationship between field theories.

Octav Cornea

Title: Some properties of the Grothendieck group of the derived Fukaya category.

Abstract: The derived Fukaya category is a triangulated category encoding symplectic rigidity properties of the Lagrangian submanifolds of a fixed symplectic manifold. In this talk, based on joint work with Paul Biran, I will discuss some properties of the associated Grothendieck group that follow from the study of Lagrangian cobordism.

Kenji Fukaya

Title: Cyclic homology in Lagrangian Floer theory and pseudo-holomorphic curve

Abstract: Cyclic homology of A-infinity algebras or categories appearing in Lagrangian Floer thoery is expected to be related to the S^1-equivariant quantum cohomology or symplectic homology of the ambient symplectic manifold. It is also important to generalize Lagrangian Floer theory including pseudo-holomorphic curves from more general bordered Riemann surfaces than a disk. I will explain these issues and some of the techniques toward establishing such results.

Kathryn Hess

Title: Cosimplicial-Simplicial models for the free loop space

Abstract: In this mini-course I will introduce various simplicial, cosimplicial, and chain complex models for free loop spaces and their structure maps and describe the relationships among these models.

  1. Simplicial and cosimplicial models

    • The cyclic nerve
    • The simplicial Hochschild construction
    • The simplicial coHochschild construction
    • The cocyclic model of Jones
  2. Chain complex models

    • Preliminaries on the bar and cobar constructions
    • The Hochschild complex
    • The coHochschild complex
    • The cyclic complex
    • The cocyclic complex
    • Hochschild cohomology

Richard Hepworth

Title: String topology of classifying spaces.

Abstract: Let G be a compact Lie group. Form the classifying space BG. Then form the space LBG of all loops in the classifying space (the strings). Finally, take the homology H_*(LBG). What is its structure? One answer, due to Chataur and Menichi, is that it is part of a "homological conformal field theory", which is an algebraic structure governed by surfaces and their diffeomorphisms. A more recent answer, due to Anssi Lahtinen and myself, is that it is part of an "h-graph field theory" where the surfaces and diffeomorphisms are replaced by much looser homotopy-theoretical versions. These lectures will go through the definitions and constructions in the case where G is finite, with lots of worked examples and so on. Lecture notes will appear on my homepage in due course, hopefully at least two weeks before the workshop.
http://homepages.abdn.ac.uk/r.hepworth/pages/

Nancy Hingston

Title: Geodesics and the structure of the free loop space

Abstract: The Chas-Sullivan product is a product on the homology of the free loop space LM of a compact oriented manifold M, the loop homology of M. If we fix a metric on M, the critical points of the length function on LM are the closed geodesics on M in the given metric. Morse theory gives a link between the geometry of closed geodesics, and the algebraic structure on the loop homology M given by the Chas-Sullivan product.
I will "review" Morse theory, then introduce the Chas Sullivan product and the “dual” cohomology product, and the fundamental inequality for the "minimax" critical level cr(X) of a homology class X on LM: cr(X∗Y) ≤ cr(X) + cr(Y).

There is a dual inequality for loop cohomology (with opposite sign!): cr(x∗y) ≥ cr(x) + cr(y).

I will discuss what the geometry of geodesics tells us about algebraic structure on LM, and what algebra tells us about geometry. Some theorems from the past are naturally stated in terms of loop products. For manifolds such as spheres and projective spaces for which there is a metric with all geodesics closed, the loop homology and cohomology rings are nontrivial, and closely linked to the geometry. For spheres we obtain significant (and so far mysterious) constraints on the critical levels of loop homology classes: for any fixed metric on a sphere there are positive constants A and B so that for each homology class X we have A deg(X) - B ≤ cr(X) ≤ A deg(X) + B.

References:

[1] R. Bott, On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171-206.
[2] M. Chas and D. Sullivan, String topology, preprint, math.GT/9911159 (1999).
[3] R. L. Cohen, J. D. S. Jones, and J. Yan. The loop homology algebra of spheres and projective spaces. In Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), volume 215 of Progr. Math., pages 77--92. Birkh¨auser, Basel, 2004.
[4] M. Goresky and N. Hingston. Loop products and closed geodesics. Duke Math. J., 150(1):117--209, 2009.
[5] N. Hingston and A. Oancea. The space of paths in complex projective space with real boundary conditions. arXiv: 1311.7292, 2013.
[6] N.Hingston and H-B Rademacher, Resonance for loop homology of spheres. J. Differential Geom. 93 (2013), no. 1, 133--174.
[7] W. Klingenberg, Lectures on Closed Geodesics, Grundlehren der mathematischen Wissenschaften 230, Springer Verlag, Berlin, 1978.
[8]. Milnor, Morse Theory, Annals of Mathematics Studies 51, Princeton University Press, Princeton N.J., 1963.

Thomas Kragh

Tittle: A simple construction of the Fukaya, Seidel, Smith - spectral sequence.

Abstract: In a paper by Fukaya, Seidel, Smith in 2007 they used a spectral sequence on A-infinity categories, induced by a filtration given by certain Lefschetz thimbles, to prove that nearby Lagrangians (spin) in a simply connected (spin) cotangent bundle are homology equivalent to the zero section. In this talk I will present a much more direct and simple construction of a similar spectral sequence and sketch an alternate proof of this. Then if time permits I will also discus how this can be generalized as Abouzaid generalized Fukaya, Seidel and Smiths proof to the non simply connected (and non spin) cases.

Janko Latschev

Title: Nonexact Liouville embeddings and symplectic homology

Abstract: I will explain how string topology type operations on symplectic homology give rise to obstructions to embedding Liouville domains into each other. The underlying argument was first outlined by Fukaya for Lagrangian embeddings, and has its roots in Gromov's original proof that there are no exact Lagrangian submanifolds in C^n. This is joint work in progress with Kai Cieliebak.

Dennis Sullivan

Title: Algebraic Models of Manifolds

Abstract: It appears that some algebraic structures associated to compact manifolds through mapping spaces like loop spaces depend only on the homotopy type of the manifold [rel boundary]. One example is the string bracket for closed three manifolds generalizing the Goldman bracket for surfaces. Since the homotopy type is a strong invariant for three manifolds the string bracket is still quite useful for example in describing the form of Thurston's geometrizationd [Chas -Gadgil largely completing a story beginning in Abbaspour's Thesis].

At the moment it is not clear whether the generalization of the Turaev cobracket to the string cobracket is homotopy invariant.This is closely related to the same question for a coproduct studied with Chas and students and independently by Goresky and Hingston.

In a slightly different and more delicate setting Basu has convinced me one can prove the corresponding coproduct really depends on the homeomorphism type of certain three manifolds.

The area where a lot of homotopy invariance is understood is related to string topology operations associated to the chains on the open moduli space of riemann surfaces. This might be termed Noncompactified String Topology. The undecided questions about the cobracket and the coproduct is part of an area which is sometimes called Compactified String Topology. Finally, the results of Basu realizing structures that detect more than homotopy type restrict attention to natural subsets of the mapping spaces and is referred to as Stratified String Topology.

Underlying all of these theories and their distinctions is the fundamental question of characterizing by algebraic structures on "Chain Complexes with Poincare Duality" Compact manifolds up to homotopy, up to homeomorphism and up to diffeomorphism.

Even a clear conceptual answer to this question is outstanding for simply connected manifolds in characteristic zero and for large dimensions.

This answer in characteristic zero might be useful in areas outside topology. One example would be studying finite dimensional algorithms that could arise using this algebraic characterization of manifolds. These algorithms would describe processes that take place in space-time like 3D fluid motion. In the middle 90's the relation of the fluid PDE's to linking and to the reconnection of closed vortex lines motivated the pictures that began the study of String Topology.

Craig Westerland

Title: Homology of stabilized moduli of Lefschetz fibrations

Abstract: This talk is about the space of relatively minimal Lefschetz fibrations over surfaces X with at most one node in each fibre. We study the homology of these spaces as the number of nodal fibres tends to infinity, and relate the stable homology to the homology of the function space of maps from X to a variant of the Deligne-Mumford compactification of M_g. Restricting our answer to H_0 yields a form of Auroux's stable classification of Lefschetz vibrations.

Partners

Irmar LMJL ENS Rennes LMBA LAREMA

Affiliation

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL