FR2962

Fédération de Recherche Mathématiques des Pays de Loire

FR CNRS 2962

A.N. Shiryaev and contemporary probability theory

Ce workshop est dédié au Professeur Albert Nikolaevich Shiryaev, qui va recevoir le titre de Docteur Honoris Causa de l'Université d'Angers, le 2 décembre 2015.

Le professeur Albert Nikolaevich Shiryaev est l’un des plus grands spécialistes mondiaux de la théorie des probabilités, de la statistique et de mathématique financière. Un parcours professionnel des plus brillants, une production scientifique hors du commun, une multitude de disciples à travers le monde et de nombreuses distinctions déjà reçues de la part de la communauté mathématique le placent également au tout premier plan sur la scène scientifique internationale.

Au cours de ce workshop des chercheurs invités et des chercheurs de la Fédération de Recherche Mathématiques de Pays de Loire présenteront leurs travaux.

SITE WEB DE LA MANIFESTATION

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Advanced Methods in Mathematical Finance

This conference is devoted to the innovations in the mathematical analysis of financial data, new numerical methods for finance and applications to the risk modeling. The topics selected include risk measures, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. During this manifestation we plan to present new models, new methods and new results in quantitative finance , to include an analysis of new financial products, to give several application-oriented presentation of mathematical finance, to cover the questions related with actuariat. More specifically, we will give priority to the following topics:

  • Actuariat and Mathematical Finance
  • Analysis of Financial markets with transation costs
  • Microstructure of the Financial markets
  • High frequency trading in Finance
  • Pricing and hedging in credit risk modelling
  • SDEs and BSDEs in Mathematical Finance
  • Stochastic analysis and its applications
  • Optimal control and its applications

Pour plus de renseignements, voir le site

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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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[Nantes]Workshop on Kähler and related geometries

[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)

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[Matpyl, Angers] Atelier "Analyse complexe et groupes de Lie"

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.).

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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. 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)

Organisers: Manfred Lehn, Christian Pauly, Christoph Sorger

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[Matpyl, Le Mans] Asymptotical Statistics of Stochastic Processes VII

Affiche_web.gifUniversité 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

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