[23b] A two-parameter family of tropical ultra-discretizations of an elliptic curve

Hiroaki Nakamura

Workshop Arithmetic & Homotopic Galois Theory 2023

[23a] A toy model of tropical ultradiscretizations of an elliptic curve,

Hiroaki Nakamura

Arithmetic Seminar Day in Toyonaka 2023 March, Osaka University　2023/03/13

[21c] On braid-types of 3-body motions on Lissajous curve

Eiko Kin, Hiroaki Nakamura, Hiroyuki Ogawa

2021/08/19

[21b] On arithmetic and geometry around the adelic Eisenstein function

Hiroaki Nakamura

RIMS workshop "Foundations and Perspectives of Anabelian Geometry", (online)　2021/06/20

[21a] Some aspects of arithmetic functions in Grothendieck-Teichm\"uller theory

Hiroaki Nakamura

Workshop "Homotopic and Geometric Galois Theory", (online) Oberwolfach, March 7-13, 2021.　2021/03/10

[18f] Adelic beta function and Eisenstein function in the Grothendieck-Teichmueller theory

Arithmetsche Geometrie Oberseminar, Universit\"at Bayreuth,December 14, 2018　2018

[18e] Topological aspects of adelic Eisenstein function

Laboratoire Paul Painlve\'e, Lille University,S\'eminaire Topologie, November 16, 2018　2018

[18d] Adelic Eisenstein function on elliptic Grothendieck-Teichmueller group

Laboratoire Paul Painlve\'e, Lille University, S\'eminaire Arithm\'etic, November 8, 2018　2018

[18c] 「グロタンディーク・タイヒミュラー理論の話題から」

第６３回 代数学シンポジウム, 東京工業大学, September 3-6, 2018.　2018

[18b] Arithmetic and combinatorics in Galois fundamental groups

Laboratoire Paul Painlve\'e, Lille University,S\'eminaire Arithm\'etic, November 8, 2018　2018

[18a] Some aspect of arithmetic of pronite fundamental groups

Mini-Workshop: Arithmetic Geometry and Symmetries around Galois and Fundamental Groups (B.Collas, P.Debes, M.Fried),Mathematisches Forschungsinstitut Oberwolfach, Germany,April 15- April 21, 2018　2018

[17a] Chebyshev type polynomials with XY-skeletons

The 1st Joint Workshop of Nanyang Technological University and Osaka University on Fundamental Science,[Parallel Session 1 Mathematics], Osaka Univeristy, September 28, 2017　2017

[16d] グロタンディーク・デッサンと周期的連分数

九州大学 数理談話会、December 15, 2016　2016

[16c] Moving frames and Eisenstein invariants

RIMS研究集会「多重ゼータ値の諸相」,京都大学数理解析研究所, July 11-14, 2016.　2016

[16b] The rep\`ere mobile and Eisenstein invariants

Laboratoire Paul Painlve\'e, Lille University,S\'eminaire Arithm\'etic, June 16, 2016　2016

[16a] 連分数と楕円曲線をわたる野鳥の森

研究集会「Tokyo Journal of Mathematics 筱田記念号刊行に寄せて」,上智大学, March 20-22, 2016　2016

[15e] 副有限 Eisenstein 商をめぐるガロア理論と数論

早稲田大学整数論セミナー, December 18, 2015　2015

[15d] Eisenstein invariant for once punctured elliptic curves

SwissMAP workshop "GRT, MZVs and associators",Les Diablerets, Switzerland, August 20-29, 2015　2015

[15c] 動く座標系とEisenstein 級数

慶應数理談話会、June 26, 2015　2015

[15b] Topology and arithmetic on the profinite Eisenstein quotient

"Geometrie, arithmetique et physique : autour des motifs "95e rencontre entre mathematiciens et physiciens theoriciens,IRMA, Univ. de Strasbourg, May 28-30, 2015.　2015

[15a] On Grothendieck dessins and elliptic curves

Seminaire d'algebre, geometrie et topologie,Laboratoire de Matheatiques J.A. Dieudonne,Universitede Nice - Sophia Antipolis,Nice, February 5, 2015　2015

[14c] Monodromy of elliptic curves and Mordell transformations in Grothendieck-Teichmueller theory

Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives II,Instituto de Ciencias Mateaticas, Universidad Autonoma de Madrid ,Madrid, December 1-5, 2014.　2014

[14b] On Grothendieck dessins and elliptic curves

Workshop "Braids and Arithmetic", CIRM, Luminy, Marseille, October 13--17, 2014.　2014

[14a] Introduction to Grothendieck-Teichmueller theory I, II,

Workshop "Braids and Arithmetic", CIRM, Luminy, Marseille October 13--17, 2014.　2014

[13d] 代数曲線のガロア・モノドロミー表現を巡るいくつかの話題

大阪大学整数論＆保型形式セミナー,October 4, 2013.　2013

[13c] Some observation in Johnson homomorphisms

Workshop "Johnson homomorphisms",University of Tokyo, May 3 - May 7, 2013.　2013

[13b] On arithmetic Dehn-Nielsen mapping

Number Theory Seminar, University of Nottingham, March 20, 2013.　2013

[13a] Arithmetic and topological problems in universal monodromy representation of Galois-Teichmueller groups

Introductory Workshop "Grothendieck-Teichm\"uller Groups, Deformation and Operads",Isaac Newton Institute for Mathematical Sciences, Cambridge,January 8-10, 2013　2013

[12d] Some open problems on profinite Dehn-Nielsen monodromy

Seminaire "Arithmetique et Topologie" a Lille,Laboratoire Paul Painleve, Universite Lille 1, November 30, 2012　2012

[12c] Ascending a tower of Galois-Teichmueller in higher genera

Seminaire "Arithmetique et Topologie" a Lille,Laboratoire Paul Painleve , Universite Lille 1, November 29, 2012.　2012

[12b] On some arithmetic monodromy invariant for once punctured torus

Workshop "Low dimensional topology and number theory IV"(organizer: Masanori Morishita), Kyushu University, Fukuoka, March 12-15, 2012　2012

[12a] 楕円曲線のEisenstein型不変量

松江数論研究集会、島根大学、Jaunuary 7, 2012　2012

[11b] Arithmetic invariants related to Eisenstein series arising from meta-abelian monodromy representations of once punctured elliptic curves

Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives, (organized by Herbert Gangl, Richard Hain, Owen Patashnick), Heilbronn Institute for Mathematical Research, Univ. of Bristol, May 3--6, 2011　2011

[11a] An introduction to moduli spaces related to elliptic curves

Heilbronn Day: Background Workshop on Multiple Zeta Values, Modular Forms & Elliptic Motives (organized by Herbert Gangl, Richard Hain, Owen Patashnick),Heilbronn Institute for Mathematical Research, Univ. of Bristol, May 2, 2011　2011

[10e] Easy walking in GT theory and anabelian geometry, II(with M. Asada, N. Takao, H. Tsunogai)

第３回日本数学会季期研究所「ガロア・タイヒミュラー理論と遠アーベル幾何の展開」The 3rd MSJ-SI "Development of Galois-Teichmueller Theory and Anabelian Geometry", RIMS, Kyoto Univ. October 25-30, 2010.　2010

[10d] Easy walking in GT theory and anabelian geometry, I(with M. Asada, N. Takao, H. Tsunogai)

第３回日本数学会季期研究所「ガロア・タイヒミュラー理論と遠アーベル幾何の展開」The 3rd MSJ-SI "Development of Galois-Teichmueller Theory and Anabelian Geometry", RIMS, Kyoto Univ. October 25-30, 2010.　2010

[10c] カルダノ・フェラーリと楕円関数論再訪

特別セミナー筑波大学, June 29, 2010.　2010

[10b] On an elliptic analgue of Ihara's power series

Workshop "Geometric and differential Galois theory", C.I.R.M., Luminy, March 29--April 2, 2010　2010

[10a] On fundamental groups of once punctured elliptic curves

Seminar "Theorie de Galois et methodes explicites" at Laboratoire Paul Painleve, Lille University, March 23, 2010　2010

[09i] Arithmetic invariants of Eisenstein type arising from fundamental groups of once punctured elliptic curves

"Final workshop" of Programme "Non-Abelian Fundamental Groups in Arithmetic Geometry" Isaac Newton Institute for Mathematical Sciences, December 14--18, 2009　2009

[09h] Tangential base point and Eisenstein power series: revisited

University of Nottingham, Nottingham, UK, December 9, 2009　2009

[09g] Computing functional equations of l-adic polylogarithms on Galois group

Workshop "Anabelian Geometry", Issac Newton Institute for Mathematical Sciences, Cambridge UK, August 24-28, 2009.　2009

[09f] Anabelian geometry VIII

Non-Abelian Fundamental Groups in Arithmetic Geometry Issac Newton Institute for Mathematical Sciences, Cambridge UK, August 14, 2012　2009

[09e] Anabelian geometry VII

Non-Abelian Fundamental Groups in Arithmetic Geometry Issac Newton Institute for Mathematical Sciences, Cambridge UK, August 13, 2011　2009

[09d] Anabelian geometry VI

Non-Abelian Fundamental Groups in Arithmetic Geometry Issac Newton Institute for Mathematical Sciences, Cambridge UK, August 12, 2010　2009

[09c] Anabelian geometry V

Non-Abelian Fundamental Groups in Arithmetic Geometry Issac Newton Institute for Mathematical Sciences, Cambridge UK, August 11, 2009　2009

[09a] Galois analogue of functional equations of polylogarithms

Workshop "The Arithmetic of Fields", Oberwolfach, Germany, February 2-6, 2009 (Oberwofach Reports 6 (2009), p.330).　2009

[09b] ガロア群と基本群、グロタンディーク予想の周辺

筑波大学数学系代数分野, June 23, 2009.　2009

[08c] Drinfeld associator と polylog 関数等式の計算,

ガロア理論とその周辺 徳島２００８, 徳島大学, September 9-12, 2008.　2008

[08b] Some topics on Grothendieck dessin and elliptic curves,

香川セミナー, May 10, 2008　2008

[08a] モーデル曲線族とGT（角皆宏氏、安田正大氏との共同研究）,

第13回早稲田大学整数論研究集会、Waseda University, March 10-12, 2008 (報告集 pp.81--82)　2008

[07e] Braid configuration spaces and Mordell covers (Part II),

"Thorie de Galois et mthodes explicites" Lille University, November 28, 2007　2007

[07d] Braid configuration spaces and Mordell covers

"GTEM Workshop Arithmetic of Curves and Covers" (Niels Borne, Pierre Debes, Michel Emsalem), Lille University, November 21-23, 2007　2007

[07c] Some selected topics on Wojtkowiak's l-adic polylogartims

夏の学校「多重ゼータ値とモティーフ」, Tohoku Univ. July 26-28, 2007　2007

[07b] A glimpse of anabelian geometry and hyperbolic varieties

"Workshop on Holomorphic Mappings, Kobayashi Hyperbolicity and Diophantine Approximation" (J.Noguchi), Tokyo University, July 20-23, 2007　2007

[07a] Grothendieck-Teichmueller group and a family of Mordell elliptic curves

Workshop "Arithmetic and Differential Galois Groups", Oberwolfach, Germany, May 14-18, 2007 (Oberwolfach Reports 4 (2007), 1493--1494)　2007

[06c] Profinite Grothendieck-Teichmueller parameters and a family of Mordell elliptic curves (joint work with H.Tsunogai)

RIMS-Workshop "Arithmetic Galois Theory and Related Moduli Spaces", Kyoto, October 23-27 & 30-31, 2006　2006

[06b] あるモーデル曲線族の組紐モノドロミーとガロア表現への応用,

熊本大学理学部数学教室談話会Kumamoto Univ., May 31, 2006　2006

[06a] Adelic beta functions and some special elliptic curves

seminar talk at Nice University, February 15, 2006　2006

[05a] Some problems in higher dimensional anabelian varieties

Mini-Workshop "Anabelian Geometry and Related Topics", 京都大学数理解析研究所、February 16-17, 2005　2005

[04d] A survey on Anderson-Ihara's adelic beta function and its elliptic analog

第４回 Galois の逆問題と Galois 被覆, 高知大学, 2004, November 2--4.　2004

[04c] 楕円曲線とブレイド群、ガロア群

研究集会「リーマン面に関連する位相幾何学」東大、Sep.28--Oct.1, 2004　2004

[04b] 曲線の moduli 空間の基本群への Galois 群の作用

2004 年度整数論サマースクール「基本群と Galois 表現」、福山、August 23--27, 2004　2004

[04a] 外ガロア表現から Grothendieck-Teichmueller 群へ --- a survey

大阪大学数学教室談話会、April 19, 2004　2004

[03l] Lemniscate braids and Grothendieck-Teichmueller group

NAKAMURA Hiroaki

Universitat Basel, Basel, Switzerland, August 11, 2003　2003

[03o] Galois 群と Grothendieck-Teichmueller 群、

香川セミナー、香川大学、December 20 - 21, 2003　2003

[03n] More equations for G_Q in GT from Bonn

Focused Research Group "Arithmetic of fundamental groups", Banff International Research Station, Banff, Canada, September 6 - 20, 2003　2003

[03m] Grothendieck-Teichmueller theory I-IV (with H.Furusho)

Durham conference on noncommutative number theory, Durham, UK, August 28 - September 5, 2003　2003

[03k] Lemniscate braids and Grothendieck-Teichmueller group,

MPI-Oberseminar, Max-Planck-Institut fur Mathematik, Bonn, August 7, 2003　2003

[03j] Galois theory of families of elliptic curves and Eisenstein series

Seminar Fundamentalgruppen und anabelsche Geometrie, Mathematisches Institut, Bonn,July 24, 2003.　2003

[03i] Galois theory of elliptic curve family and Eisenstein series, ,

Seminar on Algebra and Algebraic Number Theory, IWR, Heidelberg University, Heidelberg, July 7, 2003.　2003

[03h] l-adic polylogarithms: a survey

Journee Groupes Fondamentaux et Polylogs (P.Lochak, L.Schneps), Institut de Mathematiques de Jussieu (Paris VI), Paris, June 20, 2003.　2003

[03g] Anabelian geometry of families of elliptic curves, Eisenstein series.

Conference "Applications of Arithemetic Degeneration of Moduli" (M.Fried, H.Nakamura), University of California, Irvine, May 7-10, 2003.　2003

[03f] Some matrix representations of the parameters of the Grothendieck-Teichmueller group

Seminaire de theorie des nombres de Chevaleret,Institut de Mathematiques de Jussieu, Paris, March 10, 2003.　2003

[03e] Anabelian Geometry

Seminaire de geometrie algebrique, Nice University (topic provider with assistence of B.Toen) Nice University, March 6, 2003　2003

[03d] Monodromy in the universal elliptic curves and generalization of Rademacher functions

Nice University Feb. 28, 2003　2003

[03b] On some equations in the Grothendieck-Teichmueller group

Special Sessions "Primes and Knots" (J.Morava, S.Garoufalidis, M.Morishita), AMS-MAA Joint Mathematics Meetings, Baltimore, Jan. 15--18, 2003　2003

[03ac] Grothendieck-Teichmueller group and adelic beta functions

Algebra Seminar, University of Pennsylvania Jan. 13, 2003　2003

[02a] Exterior monodromy representations associated with elliptic curves and Eisenstein measure functions

研究集会「保型形式およびそれに付随するディリクレ級数の研究」(桂田英典),京都大学数理解析研究所, January 28 -- February 1, 2002(RIMS-講究録 1281 (2002), 176--183)　2002

[02f] Equations in the Grothendieck-Teichmueller group

Galois Theory Conference in honor of John Thompson's 70th birthday University of Florida, Nov. 4-8, 2002　2002

[02e] デデキント和とモノドロミー表現

岡山大学談話会、September 12, 2002.　2002

[02d] 楕円曲線に付随して生じる Magnus 表現と Eisenstein 級数について

第４７回代数学シンポジウム、室蘭工業大学、August 6--9, 2002　2002

[02c]Arithmetic monodromy arising from elliptic curves and generalized Dedekind sums

Workshop "Arithmetic and Differential Galois Groups"(D.Harbater, B.H.Matzat, van der Put),Mathematisches Forschungsinstitut Oberwolfach, July 8, 2002.　2002

[02b] 楕円曲線、マグナス表現と Eisenstein 級数

東京都立大学、整数論セミナー、April 16, 2002　2002

[01d] Dedekind sums, free differential calculus and anabelian geometry

Workshop "Galois theory and modular forms" Tokyo Metropolitan University September 25--29, 2001　2001

[01c] Some arithmetic in fundamental groups of affine elliptic curves

Euresco Conferences "Number Theory and Arithmetical Geometry -- Arithemetic Aspects of Fundamental Groups" (A.J.Scholl) Acquafredda di Maratea, Italy, September 1--6, 2001　2001

[01b] On explicit formula for l-adic polylogarithms

Seminar at Max-Planck-Institut fur Mathematik, Bonn, May 31, 2001　2001

[01a] Some IHX-type relations of trivalent graphs related to Morita-Mumford cohomology classes

RIMS Seminar, Kyoto University April 2, 2001　2001

[00b] On $l$-adic polylogarithms of Wojtkowiak

都立大、特異点セミナー、June 5, 2000　2000

[00a] ガロア群と基本群のべき級数表現、

都立大、整数論セミナー May 23, 2000　2000

[99e] Some aspects of Galois-Teichmueller modular groups of small type,

MSRI-workshop "Galois actions and Geometry", (P.Debes, H.Nakamura, A.Tamagawa), Berkeley, Ocotber 1999　1999

[99d] Galois group and the mapping class groups of surfaces

43rd annual meeting of the Australian Math. Soc. -- A joint meeting with the AMS, Special session "Moduli spaces of Riemann Surfaces, Mapping class groups and invariants of 3-minifolds"　1999

[99bc] リーマン面の ``キルト分割'' と Grothendieck-Teichmueller 群

東大、トポロジー火曜セミナー、 June 22, 1999　1999

[99a] ガロア・タイヒミュラーの夢

第11回 Encounter with Mathematics「曲面の写像類群 -- いろいろな数学の集いの広場」、中央大4月30日--5月1日、1999　1999

[98j] On some arithmetic equations in the Grothen\-dieck-Teich\-m\"uller group

Marseille, November 1998　1998

[98f] Pants decompositions of Riemann surfaces and systematic automorphisms of the profinite mapping class groups

Nice, France, November 1998 (colloquium talk)　1998

[98e] Galois theory in fundamental groups of affine elliptic curves

Nice, France, November 1998 (seminar talk)　1998

[98d] ガロア群と写像類群をめぐる最近のいくつかの注意 (with 角皆宏)

研究集会「リーマン面に関連する位相幾何学」（河澄響矢）、北大、September 1998　1998

[98c] Galois group over {\bf Q} moving around Teich\-m\"uller tower of all genera

ICM-1998 Satellite Conference ``Algebraic and Arithmetic Geometry'', Essen, Germany, August 1998　1998

[98b] Artin braid groups and family of elliptic curves

第７回日本数学会国際研究集会(MSJ-IRI)「類体論---その 100 年と明日への展望」(三宅克哉・他)、早稲田大学、June 1998　1998

[98a] Universal monodromy representaion and generalized Dedekind sums

研究集会「写像類群と代数曲線のモジュライ空間をめぐる新しい展開」（森田茂之）、東大、May 1998.　1998

[97d] 代数曲線の基本群に関する Grothen\-dieck 予想について(with 玉川安騎男、望月新一)

1997年度日本数学会賞秋季賞受賞講演、東大、October 1997　1997

[97c] Grothen\-dieck-Teich\-m\"uller 群のある精密化

研究集会「リーマン面に関連する位相幾何学」(河澄響矢), 北大, September 1997.　1997

[97b] Galois representations in Teich\-m\"uller modular groups

`Galois groups and Fundamental groups'(D.Harbater, Y.Ihara, B.H.Matzat), Oberwolfach, Germany, June 1997　1997

[97a] グロタンディーク・タイヒミュラー群の精密化

東京都立大学、談話会 May 8, 1997　1997

[96l] Galois-Torelli theorem for $\pi_1$ of configuration varieties of hyperbolic curves

Duke Univ. North-Carolina,USA, November 1996　1996

[96k] Tate elliptic curve and SL(2,Z)

Conference: UF-Galois theory week, Univ. of Florida, Gainesville, USA,October 1996　1996

[96j] Galois theory of moduli spaces of algebraic curves

Princeton Univ. Princeton, USA, October 1996.　1996

[96i] Galois theory and mapping class groups of surfaces

Harvard Univ., Boston, USA, September 1996.　1996

[96h] An introduction to anabelian geometry II (Part I: F.Pop)

LMS Durham symposium on `Galois representations in arithmetic algebraic geometry'(R.Taylor, A.Scholl), Durham, UK, July 1996　1996

[96g] Tangential base point and formal patching

UC Irvine, California, USA, May 1996　1996

[96f] Some recent topics on profinite arithmetic fundamental groups

UCLA, Los Angeles, California, USA, May 1996　1996

[96e] The absolute Galois group of Q and the profinite mapping class groups of surfaces

Univ. of Southern California, USA,May 1996　1996

[96d] Mapping class groups of surfaces and Galois representations

Univ. of Maryland, USA, April 1996.　1996

[96c] Galois actions on the Lickorish-Humphries generators of the mapping class groups of surfaces

Institute for Advanced Study,Princeton, USA, April 1996.　1996

[96b] `Galois story'

Torelli festival at Duke University (R.Hain), Durham, North Carolina, USA, March 1996　1996

[96a] Galois representations on profinite mapping class groups

Univ. of Pennsylvania at Philadelphia, USA, February 1996.　1996

[95e] Johnson 凖同型とガロア理論 (with M.Asada, N.Takao),

研究集会「Riemann面に関連する位相幾何学」（河澄響矢 主催）,北海道大学, June 12-16, 1995　1995

[95d] Deformation of Jacobi sum power series from a Tate elliptic curve

Math.Inst. at Heidelberg, Germany, September 1995.　1995

[95c] Limits of exterior Galois representations along maximal degeneration of curves

IWR at Heidelberg, Germany, September 1995.　1995

[95b] On universal monodromy representations of Galois-Teich\-m\"uller modular groups I, II

Conference at Luminy, ``Geometry and Arithmetic of Moduli Spaces'',France, August-September, 1995.　1995

[95a] ガロア-タイヒミュラー塔の普遍定義体について (with Y.Ihara)

研究集会「代数的整数論と数論的幾何学」数理解析研究所, December, 1994 (RIMS-講究録 925 (1995), 129--133).　1995

[94d] Geometry of braid configuration spaces of Riemann surfaces and Galois representations (with N.Takao)

Workshop on: Topology relating to Riemann surfaces (N.Kawazumi),Hokkaido Univ. September 5-9, 1994.　1994

[94c] An analogue of Tate conjecture of exterior Galois representations in pro-$l$ fundamental groups of algebraic curves

Oberwolfach, Germany, July, 1994　1994

[94e] 量指標としてのヤコビ和とその?進補間級数の紹介(after Weil, Ihara, Miki)

大阪大学整数論セミナー，June 17, 1994.　1994

[94b] Fields of definition of Teich\-m\"uller modular function fields and Oda's problem (with N.Takao, R.Ueno)

研究集会「モジュライ空間、ガロア表現および L 関数」数理解析研究所、March 1994 (RIMS-講究録 884 (1994), 112--123).　1994

[94a] Galois representations in pro-$l$ fundamental groups of punctured elliptic curves

研究集会「モジュライ空間、ガロア表現および L 関数」数理解析研究所、October 1993 (RIMS-講究録 884 (1994), 46--53).　1994

[93b] タイヒミュラー群の重み座標系と遠アーベル Tate 予想への応用 (with角皆宏)

整数論シンポジウム, 香川大, October, 1993,報告集 pp. 104--116.　1993

[93a] 副有限基本群のガロア剛性

日本数学会代数分科会特別講演,大阪府立大, September, 1993.　1993

[92b] 写像類群の自己同型に関する Ivanov の定理とその副有限アナログについて

トポロジー火曜セミナー、東大、December 1992.　1992

[92a] Rigidity, 砂田予想へのガロア理論的アプローチ

解析多様体セミナー + 幾何学コロキウム, 東大、July 1992.　1992

[90c] 球面組紐群のガロア剛性について

研究集会「代数的整数論」数理解析研究所、December 1990（RIMS-講究録 759 (1991), 25--35）　1990

[90b] $P^2-${完全四角形} の基本群のガロア自己同型について

代数学コロキウム、東大、October 1990.　1990

[90a] $P^1-\{0,1,\infty\}$ における非アーベル Tate 予想について（伊原theory の一応用）

代数学コロキウム、東大、January 1990.　1990

[89a] 代数曲線の基本群のガロア剛性について

第35回代数学シンポジウム, 北海道大学、July 1989, 報告集 186--199.　1989

[87a] 半順序集合と表現次数

研究集会「組合せ論とその周辺の研究ー可換環論、代数幾何、Lie環の表現論と半順序集合の相互関係」、数理解析研究所, October 1987(RIMS-講究録 641 (1988), 230--244).　1987

[86a] 表現次数が丁度 $p^s$ で割り切れるような $S_n$ の既約表現の個数を表す母関数について

「代数的組合せ論研究集会」愛媛大学、November 1986, 報告集 110--118　1986