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Classical Analysis
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
Seminar information archive
2012/06/27
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Daisuke Yamakawa (Tokyo Institute of Technology)
Moduli space of meromorphic connections with ramified irregular singularities on principal bundles (JAPANESE)
Daisuke Yamakawa (Tokyo Institute of Technology)
Moduli space of meromorphic connections with ramified irregular singularities on principal bundles (JAPANESE)
2011/07/08
14:30-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
T. Suzuki (Osaka Prefecture University)
$q$-Drinfeld-Sokolov hierarchy, $q$-Painlev¥'e equations, and $q$-hypergeometric functions (JAPANESE)
T. Suzuki (Osaka Prefecture University)
$q$-Drinfeld-Sokolov hierarchy, $q$-Painlev¥'e equations, and $q$-hypergeometric functions (JAPANESE)
2011/06/24
15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
J. Sekiguchi (Tokyo University of Agriculture and Technology)
A Schwarz map of Appell's $F_2$ whose monodromy group is
related to the reflection group of type $D_4$ (JAPANESE)
J. Sekiguchi (Tokyo University of Agriculture and Technology)
A Schwarz map of Appell's $F_2$ whose monodromy group is
related to the reflection group of type $D_4$ (JAPANESE)
[ Abstract ]
The system of differential equations for Appell's hypergeometric function $F_2(a,b,b',c,c';x,y)$ has four fundamental solutions.
Let $u_1,u_2,u_3,u_4$ be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map $U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y))$
is a hypersurface $S$ of the 3-dimensional projective space ${\\bf P}^3$. Then $S$ is defined by $P(u_1,u_2,u_3,u_4)=0$ for a polynomial $P(t_1,t_2,t_3,t_4)$.
It is M. Kato (Univ. Ryukyus) who determined the parameter
$a,b,b',c,c'$ such that the monodromy group of the system for $F_2(a,b,b',c,c';x,y)$ is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group $G$ of rank four by an abelian group.
In this talk, we treat the system for $F_2(a,b,b',c,c';x,y)$ with
$(a,b,b',c,c')=(1/2,1/6,-1/6,1/3,2/3$. In this case, the monodromy group is the semidirect group of $G$ by $Z/3Z$, where $G$ is the reflection group of type $D_4$. The polynomial $P(t_1,t_2,t_3,t_4)$ in this case is of degree four. There are 16 ordinary singular points in the hypersurface $S$.
In the rest of my talk, I explain the background of the study.
The system of differential equations for Appell's hypergeometric function $F_2(a,b,b',c,c';x,y)$ has four fundamental solutions.
Let $u_1,u_2,u_3,u_4$ be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map $U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y))$
is a hypersurface $S$ of the 3-dimensional projective space ${\\bf P}^3$. Then $S$ is defined by $P(u_1,u_2,u_3,u_4)=0$ for a polynomial $P(t_1,t_2,t_3,t_4)$.
It is M. Kato (Univ. Ryukyus) who determined the parameter
$a,b,b',c,c'$ such that the monodromy group of the system for $F_2(a,b,b',c,c';x,y)$ is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group $G$ of rank four by an abelian group.
In this talk, we treat the system for $F_2(a,b,b',c,c';x,y)$ with
$(a,b,b',c,c')=(1/2,1/6,-1/6,1/3,2/3$. In this case, the monodromy group is the semidirect group of $G$ by $Z/3Z$, where $G$ is the reflection group of type $D_4$. The polynomial $P(t_1,t_2,t_3,t_4)$ in this case is of degree four. There are 16 ordinary singular points in the hypersurface $S$.
In the rest of my talk, I explain the background of the study.
2011/02/18
11:00-15:45 Room #126 (Graduate School of Math. Sci. Bldg.)
T. Morita (Osaka University) 11:00-12:00
Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)
M. Yamaguchi (University of Tokyo) 13:30-14:30
Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)
(ENGLISH)
L. Di Vizio (Universite Paris 7) 14:45-15:45
Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)
(ENGLISH)
T. Morita (Osaka University) 11:00-12:00
Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)
M. Yamaguchi (University of Tokyo) 13:30-14:30
Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)
(ENGLISH)
L. Di Vizio (Universite Paris 7) 14:45-15:45
Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)
(ENGLISH)
2011/02/18
10:15-10:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Y. Ohyama (Osaka University)
Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)
Y. Ohyama (Osaka University)
Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)
2011/02/17
11:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
L. Di Vizio (Universite Paris 7) 11:00-12:00
Overview of local theory of $q$-difference equations and summation, 1
(ENGLISH)
Y. Katsushima (University of Tokyo) 13:30-14:30
Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)
K. Matsuya (University of Tokyo) 14:45-15:45
Blow-up of solutions for a nonlinear difference equation (ENGLISH)
L. Di Vizio (Universite Paris 7) 16:00-17:00
Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)
L. Di Vizio (Universite Paris 7) 11:00-12:00
Overview of local theory of $q$-difference equations and summation, 1
(ENGLISH)
Y. Katsushima (University of Tokyo) 13:30-14:30
Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)
K. Matsuya (University of Tokyo) 14:45-15:45
Blow-up of solutions for a nonlinear difference equation (ENGLISH)
L. Di Vizio (Universite Paris 7) 16:00-17:00
Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)
2011/02/16
13:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
H. Sakai (University of Tokyo) 13:30-14:30
Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)
H. Kawakami (University of Tokyo) 14:45-15:45
Degeneration scheme of 4-dimensional Painlev¥'e type equations
(Joint work with H. Sakai and A. Nakamura)
(ENGLISH)
S. Nishioka (University of Tokyo) 16:00-17:00
Solvability of difference Riccati equations (ENGLISH)
H. Sakai (University of Tokyo) 13:30-14:30
Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)
H. Kawakami (University of Tokyo) 14:45-15:45
Degeneration scheme of 4-dimensional Painlev¥'e type equations
(Joint work with H. Sakai and A. Nakamura)
(ENGLISH)
S. Nishioka (University of Tokyo) 16:00-17:00
Solvability of difference Riccati equations (ENGLISH)
2010/12/04
09:30-10:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Toshihiko Matsuki (Kyoto University)
Orbit decomposition of multiple flag varieties and representations of of quiver (JAPANESE)
Toshihiko Matsuki (Kyoto University)
Orbit decomposition of multiple flag varieties and representations of of quiver (JAPANESE)
2010/12/04
10:40-11:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Kouichi Takemura (Chuo University)
Integral transformations on the Heun equation and its applications (JAPANESE)
Kouichi Takemura (Chuo University)
Integral transformations on the Heun equation and its applications (JAPANESE)
2010/12/04
13:00-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuki Hiroe (University of Tokyo)
Weyl group symmetries of double confluent Heun equations (JAPANESE)
Kazuki Hiroe (University of Tokyo)
Weyl group symmetries of double confluent Heun equations (JAPANESE)
2010/12/04
14:10-15:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Takao Suzuki (Kobe University)
Affine root systems, monodromy preserving deformation, and hypergeometric functions (JAPANESE)
Takao Suzuki (Kobe University)
Affine root systems, monodromy preserving deformation, and hypergeometric functions (JAPANESE)
2010/12/04
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On the uniformization equations which have singularities along discriminant of complex reflection groups of rank three (JAPANESE)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On the uniformization equations which have singularities along discriminant of complex reflection groups of rank three (JAPANESE)
2010/12/03
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Daisuke Yamakawa (Kobe University)
The third Painlev¥'e equation and quiver varieties (JAPANESE)
Daisuke Yamakawa (Kobe University)
The third Painlev¥'e equation and quiver varieties (JAPANESE)
2010/06/25
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Kazuki Hiroe (University of Tokyo)
Euler transform and Weyl groups of symmetric Kac-Moody Lie algebras (JAPANESE)
Kazuki Hiroe (University of Tokyo)
Euler transform and Weyl groups of symmetric Kac-Moody Lie algebras (JAPANESE)
2010/06/17
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Teruhisa Tsuda (University of Kyushu)
On a class of the Schlesinger systems (JAPANESE)
Teruhisa Tsuda (University of Kyushu)
On a class of the Schlesinger systems (JAPANESE)
2010/05/28
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On solutions of uniformization equations (JAPANESE)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On solutions of uniformization equations (JAPANESE)
2010/04/15
16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Claude Mitschi (Univ. de Strasbourg)
The Galois group of projectively isomonodromic deformations (ENGLISH)
Claude Mitschi (Univ. de Strasbourg)
The Galois group of projectively isomonodromic deformations (ENGLISH)
[ Abstract ]
Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.
Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.
