FR2962

Fédération de Recherche Mathématiques des Pays de Loire

FR CNRS 2962

[Matpyl, Nantes] Rencontre scientifique au sein des Journées scientifiques de l’Université de Nantes

Journ__es_scient_univ_16_06.jpegLes journées scientifiques de l’Université de Nantes organisées par Jacques GIRARDEAU, Vice-Président du Conseil Scientifique de l’Université de Nantes le lundi 16 juin à la Cité internationale des congrès - Nantes-Métropole, réunira 22 porteurs de projets dans les domaines des Sciences et Techniques, Biologie-Santé, et Sciences Humaines et Sociales. Dans le domaine des sciences et techniques, le laboratoire de mathématiques Jean Leray présentera le colloque intitulé "Simulations numériques et calcul intensif"

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Cette manifestation rassemble 21 colloques scientifiques pluridisciplinaires, des stands, des posters, ainsi que 2 conférences grand public gratuites et ouvertes à tous. Pour la première fois à Nantes, près de 1500 chercheurs nantais et étrangers se réunissent. Cet événement met en lumière la richesse de la recherche développée à l'Université de Nantes.

Vous y êtes chaleureusement invités.

Au programme :

Vous êtes invités à visiter les stands de nos laboratoires et d'autres projets scientifiques. C'est une occasion unique pour échanger avec nos chercheurs.

Pour plus d'informations

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Cet événement se déroulera à la Cité des Congrès et a pour objectif de valoriser la recherche de qualité et variée développée par l’Université de Nantes.

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[Matpyl, Nantes] Journées Problèmes Inverses et Optimisation de Forme

AfficheIPSO_2008-400.jpgDans le cadre du projet ECONET avec l'Azerbaïdjan et la Géorgie, une semaine de travail sera organisée sur le thème «problèmes inverses et optimisation de forme» du 13 au 20 décembre 2008. Un moment fort de cette semaine est une conférence sur le même thème : les 17-18 Décembre 2008 : Journées Problèmes Inverses et Optimisation de Forme au Laboratoire de Mathématiques Jean Leray à l'Université de Nantes. dont l'objectif est de permettre au groupe de travail de discuter avec d'autres spécialistes dans le développement des aspects théoriques numériques de ce type de problèmes.Cette conférence est ouverte aux chercheurs et étudiants qui souhaitent y participer.

Pour visualiser le programme: Programmeipso08.pdf (274.71 Ko)

Pour visualiser l'affiche : AfficheIPSO_2008.pdf (1.37 Mo)

Liste des Conférenciers :

  • F. Aliev / Baku State University and National Academy of Sciences of Azerbaijan :

"Algorithms for some inverse optimal control problems".

  • H. Ayasso /SUPÉLEC, Paris :

"Estimation bayésienne pour le problème inverse en imagerie microonde".

  • A. Mohammad-Djafari / CNRS, SUPÉLEC, Paris :

"Probabilistic approaches to inverse problems".

  • B-N. Datta / Northern Illinois University :

"Computational and optimization methods for quadratic inverse eigenvalue problems arising in mechanical vibration and structural dynamics".

  • R. Efendiyev / IAM Baku State University :

"The one-dimensional Inverse wave spectral problem with discontinuous wave speed".

  • Y . Gasimov, A. Niftiyev, J. Zeynalov / IAMB Baku State University et A.Nachaoui / Laboratoire de Mathématiques Jean Leray Université de Nantes :

"New approach to the solution of some shape optimization and domain evolution problems".

  • Y. Jarny / LTN , Polytech’Nantes et P. Le Masson / LET2E Université de Bretagne Sud :

"Inverse heat transfer and shape identification in welding process".

  • G. Mammadova / IAM Baku State University :

"The sufficient controllability conditions for some classes of homogeneous bilinear sequential machines".

  • D. Pougaza / SUPÉLEC, Paris :

"Liens entre le problème de la tomographie X et la détermination d'une densité jointe à partir de ses marginales".

  • T. Tadumadze, A. Arsenashvili / IAM Tbilisi State University (Georgia) et A.Nachaoui / Laboratoire de Mathématiques Jean Leray Université de Nantes :

"Optimal control and inverse problems for some classes of neutral differential equations".

  • O- A. Veliev / Dogus University (Istanbul) :

"On the Inverse Problem for the Three Dimensional Schrödinger Operator with a Smooth Periodic Potential".

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[Matpyl, Nantes] Conference Mathematical Modeling and Computing in Electrocardiology.

garland_logo.pngLien du site web http://www.math.sciences.univ-nantes.fr/MMCE09/?q=node/2)

The conference will take place: June 8th-9th in Nantes.

The goal of this meeting is to gather mathematicians working in the field of modelisation, analysis, approximation, numerical analysis and scientific computing applied to electrocardiology.

Organisation :

During 2 days, a dozen of international researchers will present their work. 20 min talks reserved for Ph-D students will also be scheduled. A financial support may be granted for participating students.

Even though this conference is mainly run by mathematicians, there is a strong will of opening towards the concerned fields of biology and medical imaging, especially towards researchers and students who work on the interface between these fields and wish to strengthen their knowledge.

The first day (june 8th) is part of "Les journées scientifiques de l'université de Nantes", an annual event regrouping conferences and other scientific activities around research fields of interest in the university of Nantes.

Scientific comitee

* Y. Bourgault, Université d'Ottawa
* Y. Coudière, Université de Nantes
* M. Thiriet, Université Paris 6 et Inria
* M. Saad, Ecole Centrale de Nantes
* R. Turpault, Université de Nantes

Organisation

Y. Coudière, F. Jauberteau and R. Turpault - Université de Nantes

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[Matpyl, Angers] 2010 Workshop on Algebraïc Geometry and Physics (WAGP)

petit-Logo-Pays-de-la-Loire.gifThe Workshop will take place on June 7 to 11, 2010, in Saint Jean de Monts (Vendée, France) - see http://uk.saint-jean-de-monts.com/

This year's topic will be

DEFORMATION, QUANTIZATION, AND ALGEBRAIC INDEX THEOREMS

WAGP2010 is the 15th event of a series of Schools and Workshops that have been organized by the Mathematical Physics and Geometry group of the International School for Advanced Studies in Trieste in conjunction with leading institutions around the world. Past events have taken place in Trieste, Salamanca and Medina del Campo (Spain), Luminy (France), Como (Italy), Philadelphia (USA), Vienna (Austria), Tianjin (China), Seoul (Korea), Hangzhou (China), Maresias (Brazil). You may have a look at the past events at the following link:

http://www.sissa.it/~bruzzo/swagps/swagps.html

Deformation quantization, i.e., the study of the deformation of classical structures, such as Poisson manifolds, to noncommutative spaces, has been, together with its many applications, one of the central characters in the deep and fruitful interplay between geometry and physics that has taken place in the last 20 years. With its connections with, and applications to, noncommutative geometry, integrable systems, quantum field theory and strings, it represents a crossing point of many fundamental areas of research in present-day mathematics and theoretical physics. In the tradition of this series of events, this year's workshop aims at discussing the state of the art in this field, with a special emphasis on the mutual interactions between the physics and the mathematics communities.

Speakers: A. Alekseev, H. Bursztyn*, D. Calaque, A. Caldararu, A. D'Agnolo, G. Dito, B. Enriquez, B. Fedosov, F. Ferrari, G. Halbout, G. Landi, P. Piazza*, P. Schapira, B. Tsygan*, P. van Moerbeke

The programme will include three minicourses (two of them given by D. Calaque and A. D'Agnolo), and some contributed talks proposed by the participants. Those who want to submit a communication should send a title and a short abstract together with their registration form. Inclusion into the programme will be decided by the scientific committee.

Depending upon the outcome of our applications to funding institutions, some support may be available to PhD students and post- doctoral fellows. If you think you need support please indicate this in your application for registration.

If you are interested in participating, please write to igorre@sissa.it by January 31st, 2010.

Registered participants will receive further announcements, information about lodging and other details.

On behalf of the organizing committee, we hope you will be interested in this Workshop, and look forward to seeing you in Saint Jean des Monts.

Ugo Bruzzo Igor Mencattini Vladimir Rubtsov

Workshop web page: http://people.sissa.it/~bruzzo/wagp2010/index.htm

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[Matpyl, Nantes] Atelier de Topologie

petit-Logo-Pays-de-la-Loire.gifÀ l'occasion de la venue de Sergueï Novikov, un atelier de Topologie aura lieu le dimanche 6 juillet 2008 pm et le lundi 7 juillet tout la journée au laboratoire de Mathématiques Jean Leray à l'Université des sciences de Nantes.

La conférence de Novikov sera dans le cadre d'un colloquium le lundi 7 juillet 2008 à 15h, salle de séminaire.

  • Title:

Discrete $GL_n$ Connections and New Discretization of Complex Analysis

  • Abstract:

A few years ago new ideas were developped. How to discretize \emph{Diff-geometrical connections}? How to discretize \emph{Complex analysis}?

Our discretization is different from the classical one made for the square lattice. It is based on the ideas borrowed from the theory of completely integrable systems. We are using some remarkable properties of the equilateral triangle lattice in the euclidean plane. At the moment we are working on the extension of these ideas to the equilateral triangle lattice on the hyperbolic (Lobachevsky) plane.

Organisateur : Mr François Laudenbach, du Laboratoire Jean Leray.

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[Matpyl, Angers] The "First Angers workshop in real algebraic geometry"

petit-Logo-Pays-de-la-Loire.gifLe Laboratoire Angevin de REcherche en MAthématiques, à Angers, organise du 9 juin 2008 au 13 juin 2008, un workshop : "The First Angers workshop in real algebraic geometry"

Principaux thèmes :

  • Topology and geometry of real algebraic varieties
  • Real toric varieties
  • Linear systems on real algebraic curves
  • Singularities of real analytic mappings

Le workshop est organisé par Jean-Philippe Monnier et Adam Parusiński.

Liste des Participants:

  • Michel Coste (Rennes (I)
  • Goulwen Fichou (Rennes I)
  • Toshizumi Fukui (Saitama U., Japan)
  • Johanes Huisman (Brest)
  • Krzysztof Kurdyka (Chambéry)
  • Fréderic Mangolte (Chambéry)
  • Clint McCrory (U. of Georgia, USA)
  • Jean-Philippe Monnier (Angers)25/02/2015 - 09:45
  • Aleksandra Nowel (Gdańsk, Poland)
  • Adam Parusiński (Angers)
  • Alexandre Sine (Angers)
  • Zbigniew Szafraniec (Gdańsk, Poland)
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[Nantes, Matpyl] Activité de printemps : Fibrés vectoriels sur les courbes.

petit-Logo-Pays-de-la-Loire.gifMatpyl Spring activity on vector bundles overs curves

We will start on Monday at 9h. Registration 8h30!

This page is an overview of the topics that will be treated by the activity. Names behind the lectures indicate the distribution of the talks to be given by the participants.

Current program (PDF)

There will be 6 lectures of 45 minutes a day, scheduled as follows

09h00 - 09h45 Lecture 1
09h45 - 10h15 Coffee break
10h15 - 11h00 Lecture 2
11h15 - 12h00 Lecture 3
12h00 - 14h00 Lunch
14h00 - 14h45 Lecture 4
15h00 - 15h45 Lecture 5
15h45 - 16h15 Coffee break
16h15 - 17h00 Lecture 6

Monday

AM : Salle Hypathia

Lecture 1 [Chloé Grégoire]

  • Definition of a vector bundle over a smooth curve $X$ defined over an algebraically closed field $k$ (of any characteristic)
  • Definition of (semi-)stability of a vector bundle
  • Basic examples : if $X$ is the projective line, Grothendieck's theorem (with proof: [HL] Thm 1.3.1 ), Lazarsfeld's evaluation bundles
  • Elementary properties: stable implies simple; the category of semi-stable vector bundles of fixed slope is abelian.

References [HL],[Se],[LeP]

Lecture 2 [Arvid Perego]

  • The fundamental group $\pi_1(X)$ if $k=C$.
  • Vector bundles : $E_{\rho}$ coming from representations $\rho$ of the fundamental group .
  • Theorem of Weil (see e.g. [Se] page 46) (without proof)
  • Theorem of Narasimhan-Seshadri (without proof). Corollary: $E$ and $F$ stable implies $E \otimes F$ semi-stable

References [Se]

Lecture 3 [Heinrich Hartmann]

  • The Jordan-Hölder filtration of a semi-stable bundle
  • The Harder-Narasimhan filtration of a bundle; existence and uniqueness the Harder-Narasimhan filtration is stable under base field extension (with proof) see [HL] Theorem 1.3.7

References: [LeP] and [HL]

PM : Salle Au Val

Lecture 4 [Yashonidhi Pandey]

  • The algebraic fundamental group $\pi_1^{alg}(X)$
  • Bundles $E_\rho$ coming from continuous representations $\rho$ of the algebraic fundamental group; these are the étale trivial bundles ([LaSt])
  • The absolute/relative Frobenius morphism of the curve $X$ in positive characteristic
  • Bundles coming from representations are fixed under the Frobenius ([LaSt] Satz 1.4).

References: for general facts on the algebraic fundamental group see e.g. chapter 9 by A. Mézard in [BLR], on the relative/absolute Frobenius see e.g [Ray] section 4.

Lecture 5/6 [Christian Lehn & Markus Zowislok]

  • Definition of $(E, \nabla)$ bundle with connection $\nabla$ and $p$-curvature of $\nabla$ in char $p>0$
  • Cartier's theorem on descent under Frobenius
  • The generalized Verschiebung on vector bundles and some of its properties (without proof)
  • Frobenius-destabilized vector bundles, definition of strongly semi-stability
  • $E$ and $F$ strongly semi-stable implies $E \otimes F$ strongly semi-stable (with sketch of proof [RR]).

Reference: [K] section 5, [Ray] section 4, [LP], [RR]


Tuesday : Principal $G$-bundles

AM : Salle Eole

Lecture 1 [Manfred Lehn]

  • Review of basics in representation theory of algebraic groups (in any characteristic)
  • Definition of semi-simple/reductive algebraic groups, maximal torus, Borel subgroup, parabolic subgroup, root system, weight lattice, Weyl group

Reference: [Spr]

Lecture 2 [Tanja Becker]

  • Definition of principal $G$-bundle $E_G$ over a smooth curve $X$ with $G$ reductive.
  • Comparaison local triviality in étale topology and local trivialility in Zariski topology.
  • Extension of structure group $G \rightarrow H$, associated fibre bundle $E_G(Y)$ for an action of $G$ on $Y$, important case: $Y$ is a linear representation of $G$
  • Reduction of the structure group of $E_G$ to $H\subset G$.
  • Automorphism group $Aut(E_{G})$ of a principal G-bundle.
  • One has $Z(G)\subset Aut(E_G)$.
  • Examples: $G=GL(r)$, $SL(r), SO(r), O(r)$.

References: [So], [Ra]

Lecture 3 [Heinrich Hartmann]

  • Description of $G$-bundles $E_G$ as tannakian functor
  • Topological classification of $G$-bundle
  • Various definitions of semi-stability of $E_G$: degree of $T^{\vert}$, characters of parabolic subgroups
    $P\subset G$
  • For $G= GL(r)$ one recovers semi-stability for vector bundles.

References: [Ra], [So1], [N]

PM : Salle Au Val

Lecture 4 [Olivier Serman]

  • Semi-stable $G$-bundles with fixed topological type form a bounded family (in any characteristic)

Reference: [Beh] (8.2.6), [HN]

Lecture 5 [Jochen Heinloth]

Existence and uniqueness of canonical reduction of $E_G$ (with sketch of proof...)

References: mainly [B]; see also [BH], [AB]

Lecture 6 [Jochen Heinloth]

  • Behrend's conjecture ([B] conjecture 7.6)
  • Its implications (rationality of canonical reduction), low-height representations, and a counter-example to Behrend's conjecture for $G = G_2$ and $p=2$.

References: [B], [IMP], [He2]


Wednesday: moduli spaces

AM : Salle Hypathia

Lecture 1 [Alessandra Sarti]

  • functors of points, universal family, scheme (co-) representing a functor, existence of Grothendieck Quot scheme
  • notions de quotients (catégorique, bon, géométrique)

References: [HL] Section 2.2, section 4; [Do], [LeP]

Lecture 2 [Alessandra Sarti]

  • Introduction to GIT. Les critères utiles de semi-stabilité

References: [LeP]

Lecture 3 [Samuel Boissière]

  • Construction GIT de M(r,d)

References: [LeP]

PM Salle Hypathia

Lecture 4 [Samuel Boissière]

  • Construction GIT de M_G + propriétés

References: [BLS]

Lecture 5 [Olivier Serman]

  • Semi-stable reduction theorem(s)
  • Show that $M_X(G)$ is proper in characteristic zero or if characteristic $p$ large: do first the vector bundle case, then go to $G$-bundles.

References: [Lan], [HL] section 2B for the vector bundle case; [BP], [F], [He1] for $G$-bundles

Lecture 6 [Etienne Mann]

  • Principal $G$-bundles over elliptic curves
  • Sketch of proof that the moduli space $M_X(G)$ is isomorphic to a weighted projective space over an elliptic curve $X$

[FMW], [Las]


Thursday: Conformal blocks and Verlinde formula

AM : Salle des séminaires

Lecture 1 [Timo Schürg]

  • Introduction to moduli stacks of $G$-bundles.
  • Definition of algebraic stack, the stack of $G$-bundles is algebraic, smooth. Its dimension.

[Go], [So1]

Lectures 2/3 [Manfred Lehn]

  • Uniformization of $G$-bundles, loop spaces

References: [So1], [BL], [LS2], [F2]

PM : Salle Hypathia

Lecture 4 [Manfred Lehn]

  • Representations of affine Lie algebras,
  • space of (co)-vacua (conformal block)
  • Virasoro algebras, Sugawara construction.

[So2], [SU]

Lecture 5 [Christoph Sorger]

  • Infinite Grassmannians, line bundles over the stack of $G$-bundles

References: [So1],[So3],[BL], [LS2], [F2]

Lecture 6 [Christian Lehn]

  • Isomorphism between space of conformal blocks and space of generalized theta functions

[BL], [LS2]


Friday: projective connections, WZW and Hitchin

AM : Salle Hypathia

Lectures 1/2/3 [Christian Pauly]

  • Constructions of projective connections on the spaces of covacua by WZW and by Hitchin, comparison

PM : Salle Au Val

Lectures 4/5/6 [Christoph Sorger]

  • Fusions rings and the Verlinde formula

[Be], [So2]


Saturday: Level-Rank duality

AM : Salle Hypathia

Lecture 1/2 [Rémy Oudompheng]

  • Level-Rank (or strange) duality of theta-functions

Lecture 3 [everybody]

  • Open questions, conjectures, ideas, what to do next ...

References :

  • [AB] M.F. Atiyah, R. Bott: The Yang-Mills equations over Riemann surfaces, Phil. Trans. Roy. Soc. London A, 308 (1982), 523-615
  • [BP] V. Balaji, A.J. Parameswaran: Semistable principal bundles II. Poslrameswaran: Semis.tiona8ield-p , 3t to do next ...
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