̓Z~i[

English version here

 ꂩ̃Z~i[

 ܂ł̃Z~i[

## 1

### F2005N224i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFؑOMiF{wwj ځFʒ􉽊֐̃zbW_߂ I

v|Fʒ􉽊֐ɑ΂zbW_̍\zژ_ŁCŏ2-3͌ÓTIȃzbWE_̑w@̉sD

## 3

### F2005N414i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFؑOMiF{wwj ځFʒ􉽊֐̃zbW_߂ II

v|Fʒ􉽊֐ɑ΂zbW_̍\zژ_ŁCŏ2-3͌ÓTIȃzbWE_̑w@̉sD2ځD

## 4

### F2005N526i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFؑOMiF{wwj ځFʒ􉽊֐̃zbW_߂ III

v|Fʒ􉽊֐ɑ΂zbW_̍\zژ_ŁCŏ2-3͌ÓTIȃzbWE_̑w@̉sD3ځD

## 6

### F2005N721i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFcÍOiwoϊwj ځFs^PainlevePainleve

v|Fs^PainleveM_{\lambda}́Cd4̃O}\lambdaƃOX}lGr(2,4)̔ȑo΃~Yɂ܂s^̏ł邪ĆC15ނɕނCꂼꂪPainleve܂͂̑މɑΉĂDM_{\lambda}Painleve̎X̑މۂقړIɗłD

v|F

## 14

### F2007N118i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFAcΎiwj ځFRA[oGKZ􉽊֐̃mh~[

v|FGKZ􉽊֐GaussAppellALauricellaȂǂɂÓTIȒ􉽊֐̈ʉƂGelfandAKapranovZelevinskyɂĒꂽ􉽊֐łAϕg[bN􉽂ȂǂƖڂɊւ鋻[ΏۂȂD܂AɊ֌WĔނɂēꂽA[oƌĂ΂ΏۂA㐔􉽂gsJ􉽁AȂǂƂ̊֌WŋߔNڂW߂ĂD̃A[o̐eʂƂāARA[oicoamoebajƌĂ΂ΏۂPassareTsikhɂēꂽD܂Â͕w҂FengAHeAKennawayVafaɂđށialgaejƌĂ΂Ag[bNl̂̃~[Ώ̐Ɛ[邱Ƃ\zĂD͈̂ꂪ҂ŁAꂪGKZ^̒􉽊֐̃mh~[̌vZɖ𗧂D

## 16

### F2007N222i؁j14F00 -- 15F30 ꏊFF{ww@RȊwȁ@Ki301j utFuiwj ځFȑo΃-~Y̍ɂ

v|Fȑo΃-~Y炠̎ȖŃpF邱Ƃ͂悭mĂ邪CpF̈ʉڎwāC-~Y̍ɂčl@D

## 17

### F2007N712i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utF@ajiF{wRȊwȁCȊwuj ځF̕svc͂

v|FX̂炾1̎󐸗n܂ClɂȂ鍠ɂ͍זE̐60ɂȂ܂D̍זE̒ɂ́CtזEڂ̍זEȂǂ낢ȓ݂̂܂D1̍זE炱̂悤ȑlȍזEłdg݂T܂DɂĂCwIȔz͕@𗧂ʂƊĂ܂DC̘b̒ŊFƈꏏɒTĂƎv܂D

## 19

### F2007N1031ij16F30 ꏊFF{ww@RȊwȁ@Ki301j utFRNꎁiqwj ځFΏp-Laplace̋ǏBriot-Bouquet^藝ɂ

v|FnΏp-Laplace(rn-1|Ur|p-2Ur)r+λ rn-1|U|q-2U=0 i, 1< p,q< ∞, ╎łȂp[^[j ̋ǏiC1j̓ٓ_̋ߖT̗lq2ϐBriot-Bouquet^藝狁܂xLŋLq邱Ƃł.

## 20

### F2007N118i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFnӕFikHƑwj ځFWirtinger ϕ̈ʃW[ϊɂ

v|FWirtinger ϕƂ̓KEX̒􉽔ɑ΂ϕ\̂ЂƂłC􉽔͏㔼ʏ̈ꉿƂĈӉłDpƒ􉽔̂悭mꂽmh~[s񂪁CKȃW[Q̐ɑ΂郂W[ϊŐWsƂ݂Ȃ邱Ƃŋ߂킩D̍l𔭓WClĂ郂W[Q̈ʌɑ΂郂W[ϊǂ̂悤ɂȂĂ邩킭D̃Z~i[ł͂̈ʌɑ΂郂W[ϊیvZł̓I\邱ƂD􉽔̃mh~[s͊{Q̕\sƂđ̂ʓIł邪Čʂ͊{Q́uʌvɑ΂\s\킵ĂƍlCW[QoɒPɊ{Q͈͓̔ɂƂǂ܂Ă̂ł͓̌ʂ𓾂̂͂ȂȂςł͂ȂƎvDW[Q̈ʌɑ΂郂W[ϊl@ꂽ̂ƂẮCe[^ffLg̃G[^͂悭mĂCϊ̌WɃKEXaffLgaƂ_Iɋa邪CWirtinger ϕ̃W[ϊ̌WɂĂGȘǎCꂪOL̓aƓlɋΏۂȂ̂ǂŋߒm肽ƎvĂD

## 21

### F2007N1115i؁j16F30 ꏊFF{ww2ف@C331 utFTimur SadykoviSiberian Federal Universityj ځFDIFFERENTIAL EQUATIONS WITH PRESCRIBED FINITE MONODROMY GROUP

v|FI will present a joint work with Finnur Larusson. We state and solve a discrete version of the classical Riemann-Hilbert problem. In particular, we associate a Riemann-Hilbert problem to every dessin d'enfants. We show how to compute the solution for a dessin that is a tree. This amounts to finding a Fuchsian differential equation satisfied by the local inverses of a Shabat polynomial. We produce a universal annihilating operator for the inverses of a generic polynomial. We classify those plane trees that have a representation by M\"obius transformations and those that have a linear representation of dimension at most two. This yields an analogue for trees of Schwarz's classical list, that is, a list of those plane trees whose Riemann-Hilbert problem has a hypergeometric solution of order at most two.

## 22

### F2007N1129i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFAבiF{wj ځF_C}[zuƂ̃TvO@

v|FʃOt̊S}bO̓vI̓_C}[͌^ƂČCߔN傫ȔW𐋂D̔WɌvZ@V~[V͕s̖ʂĂDS}bO(_C}[zu)_̃ASYЉD܂C܂ł̔W̘gg̊Oɂ񕔃OtɊւ錋ʂЉD

## 23

### F2008N37ij16F30 ꏊFF{ww@RȊwȁ@Ki301j utFjFimwj ځFy[Y^CȌIɂ

v|Fy[Y^COɂẮCɎˉe@up-down generationȂǂ̎@pėlXȔmĂD{uł́Cy[Y^CȎgݍ킹I\ɂāC\荇킹@pēꂽIȌʂɂďqׂD܂Ԃ΁C֘AbɂĂGD

## 24

### F2008N1110ij16F30 ꏊFF{ww@RȊwȁ@Ki301j utFDonald A. LutziSan DiegoBwj ځFAsymptotic Integration of some classes of linear differential equations

v|FThis 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.

## 25

### F2008N129i΁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFcMiRw@wHwj ځFqpF̃bNX

v|FpF́C^̃mh~[ۂĕό邽߂̏ƂĂD CqpF̓pFqގłC ̂̑͐퍷̐ڑۂĕό邽߂̏Ƃĕ\ƂłD {uł́ĈƂɂĉD

## 26

### F2009N625i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFVladimir P. Kostovij[Xwj ځFOn the Schur-Szegö composition of polynomials

v|FThe 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

### F2009N1027i΁j16F30 ꏊFF{ww34K@iD401j utFMarius van der PutiOjQwj ځFClassification of meromorphic differential equations

v|FThe 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.

## 29

### F2009N1210i؁j16F30 ꏊFF{ww34K@iD401j utFiwj ځFReflection subgroups of Appell's F4

v|FAssume 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.

## 30

### F2010N29i΁j16F10 ꏊFF{ww@RȊwȁ@Ki301j utF֌Yi_Hwj ځFRԂ̒P^֓Rqɉēٓ_nɂ

v|FȐ̗O^Pٓ_̕όƂĂRԂ̍֓RqłB̕ނu҂͂B̍֓Rq̕Ԃ̊{Q֓AΕBł́Au҂͂̍֓RqɉӉnƂn̕ނB̂悤Ȕn̉Ԃ̎͂RłBӉn̗ގ̂̂ŉԂQɂȂ̂ނB̂悤Ȕñmh~[ƂāA{Q̂Q邢͂R ̕\B{Q̕\Ɣn̊֌WɂĘ_B

## 31

### F2010N38ij17F00 ꏊFF{ww@RȊwȁ@Ki301j utFTimur SadykoviSiberian Federal Universityj ځFBases in the solution space of the Mellin system

v|FI 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.

## 32

### F2010N527i؁j16F30 ꏊFF{ww@RȊwȁ@Ki301j utFRaimundas Vidunasi_ˑwj ځFTransformations between Heun and hypergeometric equations

v|FIt 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.

## 33

### F2010N1020ij16F30 ꏊFF{ww@RȊwȁ@Ki301j utFXؗiswbwj ځFO JacobiF3 + l (l =1,2,…) ̊mٓ_Schroedinger (Sturm-Liouville)̑

v|F3i􉽁jC4iHeunj葽̊mٓ_Fuchs^̑́C܂łقƂǒmĂȂD̘bł́C3 + l (l =1,2,…) ̊mٓ_Schroedinger (Sturm-Liouville)̉̊Sn̋̌^D́̕Ĉ悤Hamiltonian (SchroedingerpfjDarboux-Pöschl-Teller|eV
@@@ H = -d2/dx2+g(g-1)/sin2x+h(h-1)/cos2x
̕όłDŗL֌W͗O JacobiPl,n(η), n=0,1,2,…, ȂC̎deg(Pl,n)=n+l ł.@]Bochner̒藝ɂ鐧󂯂ȂD^̋Ɍ2ނ̗O LaguerreCl =1,2,…. l̕ό@ɂāCO Wilson Askey-WilsonCl =1,2,….

## 34

### F2011N24ij17F00 ꏊFF{ww@RȊwȁ@Ki301j utFRcYiHƑwj ځFCMC-1 trinoids in H3 and related objects

v|F3oȋԂ CMC-1 trinoid (퐔 0 3̎ȌȂGhϋȗ 1ł悤ȋȖ)̕ނ^CɊ֘AΏ (Iٓ_ȗ 1̌vʁC􉽔̃mh~[) Ƃ̊֘AD

## 35

### F2011N27ij17F10 ꏊFF{ww34K@iD401j utFgc͎iBwj ځFʔzu

v|FԂZ̕ʂŐ؂ƂǂȐ}邩CÑc̊􉽊w҂ɒmĂ悤ȂƂC]̗򉻂̐w҂ɂ͌\D̂悤ȂƂbɁijʔzuɂĘ_D

## 36

### F2011N1031ij16F30 ꏊFF{ww34K@iD401j utF[񎁁icmwj ځFȔ̕ϕ͉ł

v|F㐔Ïʉ̕ϕ݂͐łBʉAŴoāA㐔̉߂AϕsAϕ̎w֐ƂƂR̑LsēȂ΁A^ꂽ͉łƂBAłȂ΁A̕ϕ܂ł邱ƂؖBϕ̊bIȐɂĂqׂBc_͔̂̂Ƃ΂ŏqׂB

## 37

### F2012N26ij15F00 ꏊFF{ww@RȊwȁ@Ki301j utFRcTjiRwj ځFϐ̍

v|Fϐ̊ƂĂ悭mĂ̂̓V[Ał낤D܂D̔͑Ώ̌Q̒ʏwWƒǂDfpɑ΂đΏ̌Q̃W[\̎wWiuEA[wWjƒǂ̔𓱓āuv\D̊̊Ԃ̕ϊsɂāC̑g_IȐ𒲂ׂĂD

## 38

### F2012N27i΁j15F00 ꏊFF{ww@RȊwȁ@Ki301j utFRcTjiRwj ځFΏ̌Q̃J^sɂ܂g_

v|Fmɂ́uA^̊@wbP̃J^svl@DXN[B̌Ɋւ_ɍڂĂ\ĉCȂĂ݂ľʂ𗝉悤Ƃ݂łDN̑㐔wV|WEł̍uL^̂ŁCɉĘbĂ݂D

## 39

### F2012N119ij16F30 ꏊFF{ww34K@iD401j utFS㎁ ځF\gƃKjGn

v|F\gƂĒmĂmKdVƉłASK̎IȔi=pIȊQPII(2)̎nj ݂AQ̑̕gŌ܂SK̂Qϐ̕ΔniIȃKjGnjɂāAiPjQ̑n~gjAn~gjAnƂċLqł邱ƁAiQjn̑Ώ̐␳A iRjn̑ԂȂǂɂĂbƎv܂B ܂AKjGnƂ̊֌Wi񎩗㉻AΉ\gjɂČ݂̏󋵂Ǝv܂B

## 40

### F2012N1116ij16F00 ꏊFF{ww34K@iD401j utFgiFikCwj ځFʔzũ~i[t@Co[ɂ

v|FfȖʂ̌Ǘٓ_̃~i[t@Co[̃g|W[͌Â悭ׂĂ邪AǗٓ_łȂꍇ́Aʔzȕꍇłxb̌͊ȒPł͂ȂiႦΑg_IɃxbł邩ǂ͖łjB
@~i[t@Co[̈ꎟ̃xb̌vZ͒zu̕Ŵ̋ǏnWzW[̎߂邱ƂɋA邱ƂmĂBŋ߁ȀĂ钴ʔzȕꍇɁA\iChamberjgăxbvZASYꂽB̃ASYɊÂvZA萫IȌʂ\zȂǂЉB

## 41

### F2013N123i΁j16F30 ꏊFF{ww34K@iD401j utF{JaĎiLwj ځF̒ȖʂƗL̏̒􉽔

v|F􉽔 2F1(1/2, 1/2; 1; ) ́CPicard-Fuchs ʂĕfȉ~ȐƐ[ĂDCGreene Katz ɂēƗɓꂽuL̏̒􉽔v̂ɑΉp[^̂́CL̏̑ȉ~Ȑ̃[[^ɐ[֌W邱ƂmĂD{uł́C܂ÓTIȒ􉽔Ɋւ Katz ̌ʂɂĕK̂CL̏̒􉽔𓱓CÓTIȏꍇƂ̗ގЉD ܂Cu҂̒ȖʂƗL̏̒􉽔Ƃ̊֌WɊւŐV̌ʂɂĂbD

## 42

### F2014N513i΁j16F30 ꏊFF{ww34K@iD401j utF[񎁁icwj ځF㐔獷㐔

v|F㐔ł̐ʂ͂̌ő̍㐔̐ʂɖ|łB̗ЉB㐔IϕPoincare̒藝A\ȏpf㐔I֌WƂ咣藝i㐔IɂAmitsur̒藝jẢ̋t߂̕Kv^Harris-Sibuya̒藝ȂǁAقƂǌÓTIȌʂłB邱ƂɂĐVȐiWƎvB

̍u̓LZɂȂ܂Bueɂ܂ẮCm[g𒸂܂̂ŁCB

v|FB

v|FB

## 47

### F2015N123i؁j16F30 ꏊFF{ww34K@iD401j utF㌴liwj ځFLȖʏ̎ȓ^ʑƃGgs[ɂ

v|F{uł, LȖʏ̑oȓ^ʑɂĈʑIGgs[ĉ. ̃Ggs[Salem Ƃ΂㐔IpċLq邱ƂЉ, Ggs[lŜ̏W肵Ă. ܂, Ggs[̎ȓ^ʑeLȖʂ, 2ˉeԏ̗L_̃u[AbvɂLq邪, ̃v[Abvˉeԏ̓_zuɂĂy.

## 48

### F2016N1017ij16F30 ꏊFF{ww34K@iD401j utF㉪Ciswj ځFʕƉϕn̂Ȃ

v|Fʕ́iĵQgiO}ƂĂ͂RgjłAό^̕֐ȂǁA悢g_IIuWFNgłBAϕn͌zɏ`͊wn̂ƂłA\g_Ȃǎɐ̊ϓ_猤Ă̂łB{uł͕ʕƁAϕn̂ЂƂł闣UQ˓cqƂ̊֌WɂĉBɕʕ̊m̐ό^֐₻ʉAUQ˓cq̓璼ړ邱ƂB

bl

@diF{wwjharaoka at kumamoto-u.ac.jp
@ؑOMiF{wwjhiro at aster.sci.kumamoto-u.ac.jp