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
- 5 July 2017, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University
Saiei Matsubara (University of Tokyo)
Mellin-Barnes integral representations for GKZ hypergeometric functions of irregular singular type
- 2 July 2018, 16:30
room 301, Graduate School of Science and Technology, Kumamoto University
Raimundas Vidunas (Osaka University)
Hypergeometric expressions for modular functions
Abstract: The well-known Rogers-Ramanujan series of modular level 5 can be expressed in terms of 2F1-hypergeometric functions with the icosahedral projective monodromy. We show that similar series of level 7 can be expressed as 3F2-hypergeometric functions with the PSL(2,7) projective monodromy of 168 elements.
- 30 January 2019, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University
Davide Guzzetti (SISSA)
Non-generic isomonodromy deformations at an irregular singularity and Frobenius manifolds
Abstract: Some of the main results of [1] and [5] (see also [4] for a synthetic exposition with examples), concerning non-generic isomonodromy deformations of a certain linear differential system with irregular singularity and coalescing eigenvalues, are discussed. The results are the analytic part of a joint work with G. Cotti and B. Dubrovin. We were motivated by the problem of extending to coalescent structures the analytic theory of Frobenius manifolds, in view of the computation of the monodromy data of the quantum cohomology of Grassmannians [2], [3], [6]. Analytically, this problem translates to the problem of extending the isomonodromic deformation theory of Jimbo-Miwa-Ueno to certain non generic cases.
References
[1] G. Cotti, B. Dubrovin. D. Guzzetti: Isomonodromy Deformations at an Irregular Singularity with Coalescing Eigenvalues. arXiv:1706.04808 (2017). To
appear in Duke Math. J.
[2] G. Cotti, B. Dubrovin. D. Guzzetti: Local Moduli of Semisimple Frobenius Coalescent Structures. arXiv:1712.08575 (2017).
[3] G. Cotti, D. Guzzetti: Analytic geometry of semisimple coalescent Frobenius structures. Random Matrices Theory Appl. 6 (2017), no. 4, 1740004, 36 pp.
[4] G. Cotti, D. Guzzetti: Results on the Extension of Isomonodromy Deformations to the case of a Resonant Irregular Singularity. Random Matrices Theory
Appl. (2018).
[5] D. Guzzetti: Notes on non-generic Isomonodromy Deformations. SIGMA 14 (2018), 087, 34 pages.
[6] G. Cotti, B. Dubrovin, D. Guzzetti. Helix Structures in Quantum Cohomology of Fano Varieties. arXiv:1811.09235 (2018).
- 28 November 2019, 16:30
room 401, 3rd building of Faculty of Science, Kumamoto University
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On construction of algebraic potentials
Organizers
Yoshishige HARAOKA (Kumamoto Univ.) haraoka -at- kumamoto-u.ac.jp
Hironobu KIMURA (Kumamoto Univ.) hiro -at- aster.sci.kumamoto-u.ac.jp