[Lien vers l'affiche](http://www.math.sciences.univ-nantes.fr/~dominiqu/affiche.pdf)**Workshop on Kähler and related geometries**
[Lien vers le programme](http://www.math.sciences.univ-nantes.fr/KAEHLER09/?q=node/4)

A special trimester on Kähler and related geometries will be held at Nantes University from september 21th to december 18th 2009. The topics of interest are :

- Calabi programme, Extremal, Kähler-Einstein metrics
- Relation with stability
- Special Holonomy
- Sasakian geometry
- etc…

The trimester will consist of two events :

- An international conference
- Invitations for extended periods at Laboratoire Jean Leray throughout the trimester. Researchers are welcome to interact and to give mini lectures on their favorite topics.

[**More information for the conference**](http://www.math.sciences.univ-nantes.fr/KAEHLER09/?q=node/5)

Workshop organisé à Angers, par [Jean-Jacques LOEB](http://www.math.univ-angers.fr/~loeb/) directeur du [LAREMA](http://www.math.univ-angers.fr/spip.php?article14), qui portera sur l'interaction entre l'analyse complexe et les groupes de Lie.
Deux thèmes seront particulièrement abordés :

- La caractérisation de variétés par leur groupe d'automorphisme (après Kodama et Shimizu).

- Les structures cr homogènes (après Wang, Charbonnel et Khalgui).

Les invités sont :

- Laura GEATTI (Rome 2 )

- Andrea IANNUZZI (Rome 2)

- Marcel NICOLAU ( CRM Barcelone)

Les deux premières personnes ont beaucoup travaillé sur les actions de groupes de Liens sur les variétés complexes. Le troisième est un spécialiste des feuilletages.
Des exposés auront lieu sur les thèmes 1 et 2.

Une place très importante sera donnée aux discussions concernant ces thèmes, mais aussi de manière générale, sur les liens groupes de Lie-analyse complexe (par exemple théorie des invariants, enveloppe d'holomorphie invariante, etc.).

Le 5th Colloquium on Backward Stochastic Differential Equations, Finance and Applications sera organisé au Mans, du 18 au 20 Juin 2008, à l'Université du Maine.
[pour en savoir plus](http://www.univ-lemans.fr/~apopier/colloque/index.html)

Le 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)

Matpyl 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. Positive characteristics. Transform. Groups 8 (2003), 3-36
• [Be] A. Beauville: Conformal blocks, fusion rules and the Verlinde formula, In Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (1996)
• [BL] A. Beauville, Y. Laszlo: Conformal blocks and generalized theta functions, Comm. Math. Phys. 164 (1994), 385-419
• [BLS] A. Beauville, Y. Laszlo, C. Sorger: The Picard group of the moduli of $G$-bundles on a curve, Compositio Math. 112 (1998), 183-216
• [B] K. Behrend: Semi-stability of reductive group schemes over curves, Math. Ann. 301 (1995), 281-305
• [Beh] K. Behrend. PhD (Click to follow the link)
• [BH] I. Biswas, Y.I. Holla: Harder-Narasimhan reduction of a principal bundle, Nagoya Math. J (2004), 201-223
• [BLR] J.-B. Bost, F. Loeser, M. Raynaud: Courbes semi-stables et groupe fondamental en géométrie algébrique, Progress in Mathematics, Vol. 187, Birkhäuser Verlag
• [Do] I. Dolgachev: Lectures on Invariant Theory, London Mathematical Society Lecture Note Series 296, Cambridge University Press
• [F1] G. Faltings: Projective connections and G-bundles, J. Alg. Geometry 2, No. 3 (1993), 507-568
• [F2] G. Faltings: Algebraic loop groups and moduli spaces of bundles, J. Eur. Math. Soc. 5 (2003),41-68
• [FMW] R. Friedman, J. Morgan, E. Witten: Principal $G$-bundles over elliptic curves, Math. Res. Lett. 5 (1998), 97-118
• [Go] T. Gomez: Algebraic stacks, math.AG/9911199
• [He1] J. Heinloth: Semistable reduction for $G$-bundles over curves, J. Alg. Geom. 17 (2008), 167-183
• [He2] J. Heinloth: Bounds for Behrend's conjecture on the canonical reduction, arXiv:0712.0692
• [HN] Y. I. Holla, M. S. Narasimhan: A generalisation of Nagata's theorem on ruled surfaces, Compositio Math. 127 (2001), 321-332
• [HL] D. Huybrechts, M. Lehn: The Geometry of moduli spaces of sheaves, Aspects of Mathematics, E31 (1997)
• [IMP] S. Ilangovan, V.B. Mehta, A.J. Parameswaran: Semistability and semisimplicity in representations of low height in positive characteristic, A tribute to C.S.Seshadri
• [K] N. Katz: Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Inst. Hautes Etudes Sci. Publ. Math. 39 (1970), 175-232
• [LaSt] H. Lange, U. Stuhler: Vektorbündel auf Kurven und Darstellungen der algebraischen Fundamentalgruppe, Math. Zeitschrift 156 (1977), 73-83
• [LS] Y. Laszlo, C. Sorger: The line bundles on the moduli of parabolic $G$-bundles over curves and their sections, Ann. Sci. Ecole Norm. Sup. 4 (1997), 499-525
• [Lan] S.G. Langton: Valuative criteria for families of vector bundles on algebraic varieties, Ann. of Math. (2) 101 (1975), 88-110
• [Las] Y. Laszlo: About $G$-bundles over elliptic curves, Ann. Inst. Fourier 48 (1998), 413-424
• [LP] Y. Laszlo, C. Pauly: On the Hitchin morphism in positive characteristic, IMRN 3 (2001), 129-143
• [LeP] J. Le Potier: Lectures on vector bundles, Cambridge Studies in Advanced Mathematics 54, Cambridge University Press, 1997
• [N] M.V. Nori, The fundamental group scheme, Proc. Indian Acad. Sci. (Math. Sci.) 91 (1982), 78-122
• [RR] S. Ramanan, A. Ramanathan: Some remarks on the instability flag, Tohoku Math. Journal 36 (1984), 269-291
• [Ra] A. Ramanathan: Moduli for principal bundles over algebraic curves I, II, Proc. Indian Ac. Sci. Sci. 106 (1996), 301-328 and 421-449
• [Ray] M. Raynaud: Sections des fibrés vectoriels sur une courbe, Bull. Soc. Math. France, Vol. 110 (1982), 103-125
• [Se] C.S. Seshadri: Fibrés vectoriels sur les courbes algébriques, Astérisque 96, 1982 (rédigé par J.-M. Drézet)
• [SU] Y. Shimizu, K. Ueno: Advances in Moduli Theory, Translations of Mathematical Monographs 206, AMS (2002)
• [So1] C. Sorger: Lectures on moduli of principal $G$-bundles over algebraic curves, School on Algebraic Geometry (Trieste, ICTP 1999), 1-57
• [So2] C. Sorger: La formule de Verlinde, Séminaire Bourbaki, 1994/95, Exp. No. 794, Astérisque 237 (1996), 87-114
• [So3] C. Sorger: On Moduli for $G$-bundles for exceptional G, Ann. Sci. Ecole. Norm. Sup, 32, 1999, 127-133
• [Spr] T.A. Springer: Linear Algebraic Groups, Progress in Mathematics, Birkhäuser (1983)

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Organisers: Manfred Lehn, Christian Pauly, Christoph Sorger

Université du Maine, Le Mans, 16-19 March, 2009 The purpose of this workshop is to stimulate research in statistical inference for continuous time stochastic processes. This branch of mathematical statistics attracts more and more attention of the statisticians and probabilists because first: the real systems are often well described by the continuous time mathematical models (point processes, diffusion processes, stochastic differential equations with partial derivatives, stable processes etc.) and the second: the diversity of the models and the diversity of the statements of the statistical problems make these models quite attractive for the mathematicians because all these allow to obtain many new results which sometimes have no analogue in discrete time models.

Note that solutions obtained for continuous time models can be valid for discrete schemes of observation too. The computer realizations of the statistical algorithms (real data applications) requires that a special attention have to be payed to the effects due to discretization of continuous-time trajectories. Therefore, we wait that one (important) part of the talks will be devoted to statistical inference for discrete time observations (of continuous time systems).

Note as well, that statistical problems for stochastic processes are in the field of interests of the research teams of the universities of Rennes, Angers and Le Mans, hence this workshop can be considered as a current three-days seminaire triangulaire traditionally organized by these universities.

http://www.univ-lemans.fr/sciences/statist/liens/activites/Workshop/saps7/saps7.html

Lien vers le site web au Larema, Angers

Ce workshop réunira des chercheurs de qualité travaillant dans le domaine de risque de crédit et de martingales d'Ocone. Cette manifestation nous aidera certainement de progresser rapidement dans le domaine.

Real and complex affine algebraic geometry, first Angers 10-12 mars 2011

• lien vers le site web (Larema, Angers) http://www.math.univ-angers.fr/~mangolte/gdt-angers-2011.html

• Lien vers l'affiche : Affiche

Speakers :

H. Kraft (Basel) A. Dubouloz (Dijon)* E. Dufresne (Basel) J.-P. Furter (La Rochelle)* J. Huisman (Brest) A. Assi (Angers)* F. Mangolte (Angers)* J.-P. Monnier (Angers)* K. Kuyumzhiyan (Moscou) S. Lamy (Warwick)* P. Cassou-Nogues (Bordeaux)* M. Zaidenberg (Grenoble)

*To be confirmed

Organizers : Jean-Philippe Furter and Frédéric Mangolte

Une fonction régulue sur R^n est une fonction rationnelle prolongeable par continuité sur R^n tout entier. Les propriétés algébriques de l'anneau des fonctions régulues ainsi que les propriétés géométriques de leurs lieux d'annulation commencent à être bien comprises. Ces récents développements sont en lien avec des travaux de W. Kucharz (2009) et de J. Kollár (2011).

La classe des fonctions régulues peut-être vue comme une classe intermédiaire entre celle des fonctions algébriques et celle des fonctions arc-analytiques. Ces dernières ont été introduites par K. Kurdyka en 1988 et ont donné lieu depuis à de nombreux travaux (notamment A. Parusinski, E. Bierstone, P. Milman, G. Fichou...). Les ensembles régulus sont les fermés d'une topologie qui est plus fine que la topologie de Zariski et plus forte que la topologie arc-symétrique (lieu d'annulation des fonctions arc-analytiques).

Une série d'exposés dans des séminaires nous a convaincu de l'intérêt d'organiser une rencontre. L'objectif étant de réunir les experts en géométrie algébrique et analytique réelle intéressés par ce sujet émergent pour dresser un état de l'art et définir de nouveaux axes.

Liste préliminaire d'orateurs :

• E. Brugalle (Paris VI)
• S. Cantat (Rennes)
• M. Coste (Rennes)
• G. Fichou (Rennes)
• J. Huisman (Brest)
• W. Kucharz (Cracovie)
• K. Kurdyka (Chambéry)

• A. Parunsinski (Nice)

• Organisateurs :Jean-Philippe.Monnier@univ-angers.fr et Frédéric Mangolte

• Site web
• Affiche

Statistique Asymptotique des Processus Stochastiques VIII

Lien vers l'affiche : affiche_ASSP8.pdf (302.36 Ko)

Université du Maine, Le Mans, 21-24 March, 2011

Sponsors: Université du Maine, FR 2962 du CNRS Mathématiques des Pays de Loire, CUM, Ministère de l'Education nationale, Conseil Général de la Sarthe and Conseil Régional des Pays de la Loire

The purpose of this workshop is to stimulate research in statistical inference for continuous time stochastic processes. This branch of mathematical statistics attracts more and more attention of the statisticians and probabilists because first: the real systems are often well described by the continuous time mathematical models (point processes, diffusion processes, stochastic differential equations with partial derivatives, stable processes etc.) and the second: the diversity of the models and the diversity of the statements of the statistical problems make these models quite attractive for the mathematicians because all these allow to obtain many new results which sometimes have no analogue in discrete time models. Note that solutions obtained for continuous time models can be valid for discrete schemes of observation too. The computer realizations of the statistical algorithms (real data applications) requires that a special attention have to be payed to the effects due to discretization of continuous-time trajectories. Therefore, we wait that one (important) part of the talks will be devoted to statistical inference for discrete time observations (of continuous time systems).

Program

Participants

Scientific Programme Committee: U. Küchler, Yu. Kutoyants, N. Yoshida.

Pour en savoir plus