Journée Franco-Japonaises en honneur de Kazuo Okamoto,
Strasbourg, 10-13 November 2008

Title of Talks

Programme

Check out the official web site. The programme may be changed.

09:00-09:55 10:15-11:10
10:15-10:45 (10th)
11:20-12:15
11:00-11:55 (10th)
14:00-14:55 15:00-15:55 16:30-17:25
10th J.-P. Ramis*1 M. Mazzocco*2 J. Sauloy A. Granier L. Di Vizio
11th H. Tahara S. Malek H. Sakai K. Okamoto F. Loray D. Bertrand
12th K. Iwasaki O. Lisovvy Y. Ohyama
13th B. Malgrange L. Teyssier K. Takemura H. Kimura V. Heu R. Conte
10th 09:00~ reception
10th 10:00~ Ouverture

*1) 10:15-10:45
*2) 11:00-11:55


Title of Talks

Daniel Bertrand (Paris) On Manin's kernel theorem
Robert Conte (Cachan) Elliptic general analytic solutions
Lucia di Vizio (Paris) q-difference equations with |q|=1
Anne Granier (Toulouse) A Galois D-groupoid for q-difference systems
Viktoria Heu (Rennes) Isomonodromic deformations and maximally stable bundles
Katsunori Iwasaki (Kyushu) Periodic solutions to Painlevé VI
Hironobu Kimura (Kumamoto) On the Schlesinger systems and their particular solutions of hypergeometric type
Oleg Lisovyy (Tours) Algebraic solutions of the sixth Painleve equation
Frank Loray (Rennes) Dynamics on character varieties and irreducibility of the Painlevé VI equation
Stéphane Malek (Lille) On Gevrey functions solutions of partial differential equations with fuchsian and irregular singularities
Bernard Malgrange (Grenoble) Differential algebraic groups
Marta Mazzocco (Manchester) Hankel determinant formulae for the Painlevé equations
Kazuo Okamoto (Tokyo)
Yousuke Ohyama (Osaka) Linear monodromy of the Painlevé transcendents
Jean-Pierre Ramis (Toulouse) From Painlevé to Okamoto
Hidetaka Sakai (Tokyo) Monodromy preserving deformation and 4-dimensional Painlevé type equations
Jacques Sauloy (Toulouse) The local q-difference Galois group : what it is and what it acts on
Hidetoshi Tahara (Sophia) On a reduction of Briot-Bouquet type partial differential equation in a resonant cases
Loïc Teyssier (Strasbourg) A tentative definition of the local Painlevé property for complex foliations
Koichi Takemura (Yokohama City Univ) Heun's equation and the space of initial conditions for Painleve VI

Daniel Bertrand (Paris)

Title: On Manin's kernel theorem


Robert Conte (Cachan)

Title: Elliptic general analytic solutions


Lucia di Vizio (Paris)

Title: q-difference equations with |q|=1


Anne Granier (Toulouse)

Title: A Galois D-groupoid for q-difference systems


Viktoria Heu (Rennes)

Title: Isomonodromic deformations and maximally stable bundles


Katsunori Iwasaki (Kyushu)

Title: Periodic solutions to Painlevé VI

Abstract: We consider the periodic solutions of the sixth Painlevé equation along a given loop. For any non-elementary loop we show that the number of isolated periodic solutions grows exponentially as the period tends to infinity, where the growth rate can be explicitly determined from the loop. We also show that asymptotically almost all isolated periodic solutions are saddle periodic solutions. This is a joint work with Takato Uehara.

Hironobu Kimura (Kumamoto)

Title:


Oleg Lisovyy (Tours)

Title: Algebraic solutions of the sixth Painlevé equation

Abstract: I will describe all finite orbits of an action of the extended modular group on conjugacy classes of SL(2,C)-triples. The result will then be used to classify algebraic solutions of the general Painlevé VI equation up to parameter equivalence.

Frank Loray (Rennes)

Title: Dynamics on character varieties and irreducibility of the Painlevé VI equation

Abstract: This is a joint work with Serge Cantat. We consider representations of the fundamental group of the 4-punctured sphere into SL(2,C). The moduli space of representations modulo conjugacy into SL(2,C) is the character variety. The Mapping Class Group acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. We prove the absence of invariant affine structure or invariant foliation for this dynamical system. this implies, following results of Casale, that the Galois groupoid of the Painlevé VI foliation (in the sense of Malgrange) is not smaller than the symplectic groupoid, providing a new proof of the transcendence of Painlevé solutions.

Stéphane Malek (Lille)

Title: On Gevrey functions solutions of partial differential equations with fuchsian and irregular singularities

Abstract: We construct formal power series solutions of non linear partial integro-differential equations with fuchsian and irregular singularities at the origin in C2 for given initial conditions being formal power series. We give sufficient conditions under which there exist actual sectorial holomorphic solutions which are Gevrey asymptotic to the given formal series solutions for given 1-summable formal series initial conditions. A phenomenon of small divisors is observed for the appearance of singularities of the Borel transform of the constructed formal series due to the presence of the fuchsian singularity. This property has an effect on the Gevrey order asymptotic for the constructed holomorphic solutions which becomes larger than the Gevrey order of the initial conditions.

Bernard Malgrange (Grenoble)

Title: Differential algebraic groups


Marta Mazzocco (Manchester)

Title: Hankel determinant formulae for the Painlevé equations


Kazuo Okamoto (Tokyo)

Title:


Yousuke Ohyama (Osaka)

Title: Linear monodromy of the Painlevé transcendents

Abstract: The Painlevé equations can be derived from monodromy preserving deformations. In general, however, it is difficult to calculate monodromy data (linear monodromy) explicitly. We show that for some Painlevé functions the linear monodromy can be exactly determined. More precisely, we determine the linear monodromy of Painlevé transcendents which are analytic around fixed singular points. We also study analytic solutions of q-PVI, which is given by a connection preserving deformation of a certain q-difference linear equation.

Hidetaka Sakai (Tokyo)

Title: Monodromy preserving deformation and 4-dimensional Painlevé type equations


Jacques Sauloy (Toulouse)

Title: The local q-difference Galois group : what it is and what it acts on


Hidetoshi Tahara (Sophia)

Title: On a reduction of Briot-Bouquet type partial differential equation in a resonant case


Loïc Teyssier (Strasbourg) 

Title: A tentative definition of the local Painlevé property for complex foliations


Koichi Takemura (Yokohama City Univ)

Title: Heun's equation and the space of initial conditions for Painlevé VI


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