Seminar on Global Analysis

Japanese version here



24 February 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Hironobu KIMURA (Kumamoto Univ.)
Toward the Hodge theory for general hypergeometric functions - I



10 March 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Susumu TANABE (Kyushu Univ.)
On uniformisation of discriminantal loci for complete intersections



14 April 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Hironobu KIMURA (Kumamoto Univ.)
Toward the Hodge theory for general hypergeometric functions - II



26 May 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Hironobu KIMURA (Kumamoto Univ.)
Toward the Hodge theory for general hypergeometric functions - III



15 June 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Masafumi YOSHINO (Hiroshima Univ.)
Exact asymptotic analysis for non-linear partial differential equations



21 July 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Yoshihiro MURATA (Nagasaki Univ.)
Matrix Painleve equations and Painleve equations



16 September 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Sayaka HAMADA (Yatsushiro National College of Technology)
On Baker-Forrester's constant term conjecture



10 October 2005, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Galina FILIPUK (Kumamoto Univ.)
On middle convolution and the Painleve equations



27 January 2006, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Yusuke SASANO (Kobe Univ.)
Higher order Painleve equations of types Al(1), Bl(1), Cl(1), Dl(1)



10 February 2006, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Joichi KANEKO (Ryukyu Univ.)
On some extremum problem due to Selberg



10 May 2006, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Robert Conte (CEA-Saclay, France)
On the Lax pairs of the sixth Painleve equation
Abstract: here



16 November 2006, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Katsuhisa Mimachi (Tokyo Institute of Technology)
Connection problem associated with Selberg type integrals and Racah polynomials



21 December 2006, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Yusuke Sasano (Univ. of Tokyo)
Friends of the Garnier system in two variables and an extension of the Okamoto transform



18 January 2007, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Kazushi Ueda (Osaka Univ.)
Coamoeba and the monodromy of GKZ hypergeometric function



15 February 2007, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Mitsuhiko Kohno (Kumamoto Univ.)
Gauss multiplication formula for extended Psi-function



22 February 2007, 14:00
room 301, Graduate School of Science and Technology, Kumamoto University

Hiroshi Kawakami (Univ. of Tokyo)
On higher dimensional anti self-dual Yang-Mills equation



12 July 2007, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Kazufumi Takamune (Dep. Biology, Kumamoto Univ.)
Toward the analysis of the development of multicellular organisms



31 October 2007, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Koichi Uchiyama (Sophia Univ.)
On local solutions of spherically symmetric p-Laplace equation and the theorem of Briot-Bouquet type



8 November 2007, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Humihiko Watanabe (Kitami Institute of Technology)
General modular transformation for Wirtinger integral



15 November 2007, 16:30
room C331, Faculty of Science, Kumamoto University

Timur Sadykov (Siberian Federal University)
DIFFERENTIAL EQUATIONS WITH PRESCRIBED FINITE MONODROMY GROUP



29 November 2007, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Taizo Sadahiro (Prefectural University of Kumamoto)
Dimer configuration and sampling methods



7 March 2008, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Fumihiko Nakano (Kochi University)
Elementary properties of Penrose tiling



10 November 2008, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Donald A. Lutz (San Diego State University)
Asymptotic Integration of some classes of linear differential equations

Abstract: This talk will involve theorems which have been used for obtaining asymptotic representations for solutions of several different kinds of second order linear differential equations. The methods used to obtain the results originally were quite ad hoc and depended heavily on the special structure of the equations. It will be shown how the results can also be obtained from a more unified perspective as part of a general theory for systems of linear differential equations originated by N. Levinson. In doing so, the results can in many cases also be improved and extended.


9 December 2008, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Mikio Murata (Aoyama Gakuin University)
Lax form for q-Painleve equations



25 June 2009, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Vladimir P. Kostov (Universite de Nice-Sophia Antipolis)
On the Schur-Szegö composition of polynomials

Abstract: The Schur-Szegö composition (SSC) of the degree n polynomials P:=∑j=0najxj and Q:=∑j=0nbjxj is the polynomial P*Q:=∑j=0najbjxj/Cnj. We recall first some classical results. When the polynomials are hyperbolic, i.e. with all roots real, and when all roots of P have the same sign, then the multiplicity vector of P*Q is completely defined by the multiplicity vectors of P and Q. When both P and Q have all their roots negative, then the SSC defines a semi-group action on the set of multiplicity vectors considered as ordered partitions of n.
If a (complex) polynomial P has one of its roots at -1, then it is representable as an SSC of n-1 polynomials of the form (x+1)n-1(x+ai) where the numbers ai are uniquely defined up to permutation. We shall discuss some properties of the mapping sending the symmetric polynomials of the roots of P into the ones of the numbers ai.

27 October 2009, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Marius van der Put (University of Groningen)
Classification of meromorphic differential equations

Abstract: The classification of linear differential equations over the field K=C({z}) of the meromorphic functions at z=0 (i.e., the field of the convergent Laurent series) is a highlight of the theory of asymptotics. Starting with simple examples we will give a survey of this and show how this leads to explicit monodromy spaces. The relation with a theorem of Sibuya and the fundamental paper of Jimbo-Miwa-Ueno will be discussed.

17 November 2009, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Masaaki Yoshida (Kyushu University)
Problems of geometry arising from hypergeometric function



10 December 2009, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Mitsuo Kato (University of the Ryukyus)
Reflection subgroups of Appell's F4 monodromy groups

Abstract: Assume the system of differential equations E4(a,b,c,c';X,Y) satisfied by Appell's hypergeometric function F4(a,b,c,c';X,Y) has a finite irreducible monodromy group M4(a,b,c,c'). The monodromy matrix Γ3* derived from a loop Γ3 once surrounding the irreducible component C={(X,Y)|(X-Y)2-2(X+Y)+1=0} of the singular locus of E4 is a complex reflection. The minimal normal subgroup NC of M4 containing Γ3* is, by definition, a finite complex reflection group of rank four. Let P(G) be the projective monodromy group of the Gauss hypergeometric differential equation 2E1(a,b,c). It is known that NC is reducible if ε:=c+c'-a-b-1∉Z or if ε∈Z and P(G) is a dihedral group. We prove that if ε&isinZ, then NC is the (irreducible) Coxeter group W(D4), W(F4), W(H4) according as P(G) is a tetrahedral, octahedral, icosahedral group, respectively.

9 February 2010, 16:10
room 301, Graduate School of Science and Technology, Kumamoto University

Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On systems of differential equations with singular locus along Saito free divisors of simple type in 3-dimension space



8 March 2010, 17:00
room 301, Graduate School of Science and Technology, Kumamoto University

Timur Sadykov (Siberian Federal University)
Bases in the solution space of the Mellin system

Abstract: I will present a joint work with Alicia Dickenstein. We consider algebraic functions z satisfying equations of the form
a0 zm + a1zm1 + a2 zm2 + … + an zmn + an+1 =0.
Here m > m1 >… > mn>0, m,mi N, and z=z(a0,…,an+1) is a function of the complex variables a0, …, an+1. Solutions to such equations are classically known to satisfy holonomic systems of linear partial differential equations with polynomial coefficients. In the talk I will investigate one of such systems of differential equations which was introduced by Mellin. We compute the holonomic rank of the Mellin system as well as the dimension of the space of its algebraic solutions. Moreover, we construct explicit bases of solutions in terms of the roots of initial algebraic equation and their logarithms. We show that the monodromy of the Mellin system is always reducible and give a formula for the holonomic rank of a generic bivariate hypergeometric system.

27 May 2010, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Raimundas Vidunas (Kobe University)
Transformations between Heun and hypergeometric equations

Abstract: It is known that Heun's functions (or differential equations) can be reduced to Gauss hypergeometric functions by rational changes of its independent variable only if its parameters, including the fourth singular point location parameter t and the accessory parameter, take special values. The talk will present a classification of Heun functions reducible to Gauss hypergeometric functions via such transformations. Some arithmetic properties of the parameter t will be noted.

20 October 2010, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University

Ryu Sasaki (Kyoto University)
Exceptional Jacobi polynomials -- global solutions of a Schroedinger equation with 3+l regular singular points



4 February 2011, 17:00
room 301, Graduate School of Science and Technology, Kumamoto University

Kotaro Yamada (Tokyo Institute of Technology)
CMC-1 trinoids in H3 and related objects




7 February 2011, 17:10
room 401, 3rd building of Faculty of Science, Kumamoto University

Masaaki Yoshida (Kyushu University)
Plane arrangements




31 October 2011, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Keiji Nishioka (Keio University)
Solvability of variational equations of solvable differential equations




6 Feburary 2012, 15:00
room 301, Graduate School of Science and Technology, Kumamoto University

Hirofumi Yamada (Okayama University)
Mixed basis for polynomial ring in infinitely many variables




7 Feburary 2012, 15:00
room 301, Graduate School of Science and Technology, Kumamoto University

Hirofumi Yamada (Okayama University)
Combinatorial theory on Cartan matrix for symmetric groups




9 November 2012, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Yusuke Sasano
Soliton equations and Garnier system




16 November 2012, 16:00
room 401, 3rd building of Faculty of Science, Kumamoto University

Masahiko Yoshinaga (Hokkaido University)
On Milnor fibers for real hyperplane arrangements




3 December 2013, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Kazuaki Miyatani (Hiroshima University)
Certain hypersurface and hypergeometric function on a finite field




13 May 2014, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Keiji Nishioka (Keio University)
From differential algebra to difference algebra




11 June 2014, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Hiroshi Yamazawa (Shibaura Institute of Technology)
Holomorphic and singular solutions of q-analogue of the Briot-Bouquet type equations




26 June 2014, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Masatoshi Noumi (Kobe University)
On Okubo's formula




27 October 2015, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
Introduction to Flat Structure




17 November 2015, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Ko-ki Ito (Toyohashi University of Technology)
System of linear differential equations singular along a dual curve




3 December 2015, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Takato Uehara (Saga University)
Automorphisms of rational surfaces and entropies




17 October 2016, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University

Shuhei Kamioka (Kyoto University)
Plane partitions and integrable systems




Organizers

 Yoshishige HARAOKA (Kumamoto Univ.) haraoka -at- kumamoto-u.ac.jp
 Hironobu KIMURA (Kumamoto Univ.) hiro -at- aster.sci.kumamoto-u.ac.jp