【 著書 】
２０２４年１月２３日更新．
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専門書．
[b4]: Goo Ishikawa, Singularities of Curves and Surfaces in Various Geometric Problems,
CAS Lecture Notes 10, Exact Sciences, 2015.
[b3]:「２１世紀の数学」幾何学の未踏峰，日本評論社，2003, (問題執筆)．
[b2]: 代数曲線と特異点，共立出版，2001, (共著)．
[b1]: 応用特異点論、共立出版、1998, (共著)．
訳書．
[T1]: D.マクラガン, B.シュツルムフェルズ「トロピカル幾何学入門」丸善出版， (2023) （共訳） ．
教科書．
[t6]: 「微積のあたま」共立出版，2022．（単著）．
[t5]: 「位相のあたま」共立出版，2018．（単著）．
[t4]:
「論理・集合・数学語」共立出版，2015．（単著）．
[t3]: 「愛ではじまる微積分」プレアデス出版，2008．（単著）．
数年前の講義ノートで OCW にも採用されたものを，大幅に加筆して仕上げた本．
正誤表ver.3
(pdf)
[t2]: 線形写像と固有値、共立出版、1996、(共著)．
[t1]: 行列と連立一次方程式、共立出版、1996、(共著)．
啓蒙書．
[e4]: 「よろず数学問答」日本評論社，2008．（単著）
[e3]: 北大高校生講座「数学の並木道」，中村郁監修，日本評論社，2004, (分担執筆)．
[e2]: 大学でどのような数学を学ぶのか，数学セミナー編集部編，日本評論社，2002, (分担執筆)．
[e1]: ヒルベルト 23 の問題、杉浦光夫編、日本評論社、1997、(分担執筆)．
教育啓蒙的講演
石川 剛郎，「トポロジーの考え方」
北海道後志管内高等学校数学教育研究会，小樽商業高校，小樽，日本．
２００７年１１月９日．
石川 剛郎，「大学一年生が数学の授業でする質問・抱く疑問」
北海道地区数学教育協議会，第６１回数学教育実践研究会，北大，日本．
２００７年６月２日．
講演記録．２０２３年１２月３日更新
[217]
Goo Ishikawa, Legendre singularities of sub-Riemannian geodesics and related topics,
February 18th 2024,
接触構造，特異点，微分方程式及びその周辺
January 16-18th. 2024,
金沢大学サテライト・プラザ, Kanazawa, Japan (Online presentation).
[216]
Goo Ishikawa, Singular curves of (3,5)-distributions,
November 27th 2023,
Extension of the Singularity theory,
November 27--29, 2023,
RIMS, Kyoto University, Japan.
[215]
Goo Ishikawa, Singularity theory over dual numbers,
Shizuoka Univ. March 30th 2023,
28st (Numadu)-Shizuoka Workshop -- Geometry, Mathematical Physics and Quantum Theory,
29th-31st March 2023, Shizuoka, Japan.
[214]
Goo Ishikawa, Singular curves of (4,7) distributions, Shizuoka Univ. March 29th 2023,
28st (Numadu)-Shizuoka Workshop -- Geometry, Mathematical Physics and Quantum Theory,
29th-31st March 2023, Shizuoka, Japan.
[213]
Goo Ishikawa, (4,7) distributions and algebraic curves on tori, March 8th 2023,
Singularity theory of Differentiable
mappings and its applications,
March 6th-8th 2023, Faculty of Sciences, Hokkaido University, Sapporo, Japan.
[212]
Goo Ishikawa, Frontal Jets, Marth 7th 2023,
Singularity theory of Differentiable
mappings and its applications,
March 6th-8th 2023, Faculty of Sciences, Hokkaido University, Sapporo, Japan.
[211]
Goo Ishikawa, Singularity theory over dual numbers, March 6th 2023,
Singularity theory of Differentiable
mappings and its applications,
March 6th-8th 2023, Faculty of Sciences, Hokkaido University, Sapporo, Japan.
[210]
Goo Ishikawa,
Singularity theory of mappings over dual numbers, February 21st, 2023,
Singularity theory of Differentiable mappings and its applications, February 20th--22nd, 2023,
Nihon University, Japan.
[209]
Goo Ishikawa,
Legendre singularities of sub-Riemannian geodesics,
3rd October 2022,
Singularity theory and its applications,
RIMS-Sing 1 Workshop,
Room 420, Research Institute for Mathematical Sciences,
Kyoto University, Japan.
October 3rd--5th 2022.
[208]
Goo Ishikawa,
Singular curves of $(4, 7)$ distributions and C_3,
October 1st, 2022,
Correspondences of various geometries,
Faculty Science, Nara Women's University,
September 30th -- October 2nd 2022.
[207]
Goo Ishikawa, Singular curves of $(4, 7)$ distributions,
June 16th 2022,
Application of singularity theory to topology,
differential geometry and related area, June 16th--18th 2022. (Online workshop).
[206]
Goo Ishikawa,
Singularities of parallels to tangent developable surfaces,
28 December 2021,
24-th Petrovskii Conference,
Differential Equations and Related Topics,
Dec. 26 -- Dec. 30, 2021.
[205]
Goo Ishikawa,
Singularities of parallels to tangent developable surfaces,
25 June 2021. The Future of Singularity Theory 24 June -- 26 June. 2021 (Online Workshop).
[204]
Goo Ishikawa,
Singularities of parallels to tangent developable surfaces, (online Lecture)
The Sao Carlos Singularity Theory Webinar, UFSCar and ICMC - USP,
9th June 2021.
[203] Goo Ishikawa, Singularities of parallels to tangent maps of frontals, (Poster presentation),
16th International Workshop on Real and Complex Singularities -- celebrating 30 years,
organised by Singularity Theory Group, Sao Carlos - Brazil,
On-line edition, 23--30 November 2020.
[202]
Goo Ishikawa,
Tangential and Normal Maps to Frontals, (Poster presentation),
The International Conference on
Differential Equations and Dynamical Systems 2020 (DIFF2020),
organised by Steklov Mathematical Institute of Russian Academy of Sciences,
Vladimir State University and
Lomonosov Moscow State University,
3rd--8rd July 2020,
[201]
Goo Ishikawa,
On Normal and Tangential Maps
to Frontals,
22nd October 2019,
6th International Workshop on
Singularities in Generic Geometry and its Applications
VALENCIA VI,
the Campus de Burjassot of the Universitat de Valencia.
21st -- 25th October 2019, Valencia, Spain.
[200]
Goo Ishikawa,
Several problems on singularities of
implicit differential equations
and related topics,
September 9, 2019,
INTERNATIONAL CONFERENCE
Singularity Theory and its Applications in Differential Equations and Differential Geometry
September 8-14, 2019,
Lomonosov Moscow State University (Department of Mechanics and Mathematics, chair of dynamical systems),
Moscow, Russia.
[199]
Goo Ishikawa,
A remark on the geometric theory of third order ordinary differential equations,
(in Japanese),
20 August, 2019,
Muroran Workshop,
20 August --- 21 August, 2019,
Muroran Institute of Technology, Muroran, Japan.
[198]
Goo Ishikawa, Motoki Oyama,
Topology of complements to
real affine space line arrangements,
March 22nd 2019,
Special Session on Real and Complex Singularities
Spring Central and Western Joint Sectional Meeting, AMS,
University of Hawaii at Manoa, Honolulu, Hawaii, USA,
March 22nd -- 24th 2019.
[197]
Goo Ishikawa,
Cofrontals,
December 6th 2018,
Research on topology and differential geometry
using singularity theory of differentiable maps,
RIMS, Kyoto University, Japan,
December 4th -- 7th 2018.
[196]
Goo Ishikawa,
Leibniz complexity of Nash functions on differentiations,
September 13th 2018.
Real Algebraic Geometry and Singularity
Theory Symposium
(Memorial Conference of Masahiro Shiota),
Hyokyo Hall, Kobe Information Culture Building 3F
Kobe Harborland Campus of Hyogo University of Teacher Education,
September 11th -- 13th 2018.
[195]
Goo Ishikawa,
Topics on frontal singularities,
26 July 2018,
15th International Workshop
on Real and Complex Singularities, Sao Carlos, Brazil,
22 - 28 July 2018.
[194]
Goo Ishikawa,
Contact structures, Lagrangian cone structures
and (2,3,5)-distributions,
July 7th 2018, North Kyushu Geometry Workshop 2018,
Tobata Campus, Kyushu Institute of Technology, Kokura, July 7th 2018.
[193]
Goo Ishikawa,
Duality of (2,3,5)-distributions and
Lagrangian cone structures,
March 7th 2018, (Numazu-)Shizuoka workshop --- Geometry, Mathematical Physics and
Quantum Theory, Shizuoka University, March 6--8, 2018.
[192]
Goo Ishikawa,
Duality of (2,3,5)-distributions and
Lagrangian cone structures,
January 26th 2018,
Contact structure, Singularities, Differential equations and related area,
Satellite Plaza of Kanazawa University, Kanazawa, Japan.
[191]
Goo Ishikawa, Stability of parametric Lagrangian and Legendrian varieties,
December 13 (2017).
International Conference on Singularity Theory
and Dynamical Systems|in Memory of John Mather,
Tsinghua Sanya International Mathematics Forum
Yau Mathematical Sciences Center, Tsinghua University
三亜, 海南島, 中国, December 11--15, (2017).
[190]
Goo Ishikawa, Stability of Frontal Singularities,
RIMS，Kyoto, JAPAN, 28 November 2017.
RIMS 共同研究(公開型)
可微分写像の特異点論の局所的研究と大域的研究
京都大学数理解析研究所，２０１７年１１月２８日．
[189]
Goo Ishikawa, Duality-singularity of indefinite metrics and contact structures,
1 August 2017,
Singularities in Generic Geometry and its Applications: Valencia V,
Facultad de Ciencias, UNAM, Mexico City,
31 July -- 4 August 2017.
[188]
Goo Ishikawa,
Duality of (2,3,5)-distributions and Lagrangian cone structures,
July 16 2017,
The memorial workshop for the retirement of Professor Keizo Yamaguchi,
July 14 -- July 16 2017, Kobe University, Kobe, Japan.
[187]
Goo Ishikawa,
Recognition Problem of Frontal Singularities,
June 1 2017,
Applications of Differential Geometry and Singularity Theory,
June 1 -- June 3, 2017, Iwate Medical University, Morioka, Japan.
[186]
Goo Ishikawa, Duality-singularity of indefinite metrics and contact structures,
March 8 2017,
24th Numazu conference,
March 6 -- March 8, 2017,
Numazu College of Technology, Shizuoka, Japan.
[185]
Goo Ishikawa, Duality-singularity of indefinite metrics and contact structures,
20 January 2017,
Contact structure, Singularities, Differential equations and related area,
Satellite Plaza of Kanazawa University, Kanazawa, Japan.
[184]
Goo Ishikawa, Yoshinori Machida, Masatomo Takahashi,
Null frontal singular surfaces in Lorentzian 3-spaces,
VIII International Meeting on Lorentzian Geometry
Malaga (Spain), 20--23 September 2016.
(poster presentation).
[183]
Goo Ishikawa, Tatsuya Yamashita,
Affine connections and singularities of tangent surfaces of space curves (in Japanese),
18th March 2016, MSJ Spring Meeting 2016,
16th March -- 19 March 2016, University of Tsukuba, Tsukuba, Japan.
[182]
Goo Ishikawa, Tatsuya Yamashita,
Leibniz complexity of Nash functions on differentiations (in Japanese),
16th March 2016, MSJ Spring Meeting 2016,
16th March -- 19 March 2016, University of Tsukuba, Tsukuba, Japan.
[181]
Goo Ishikawa,
Maps of singularity theory (in Japanese),
12th March 2016, Encounter of Singularities with Geometry, Encounter with Mathematics,
12th--13th March 2016, Chuo University, Tokyo, Japan
[180]
Goo Ishikawa,
Neutral metrics, rolling-bodies and the Kepler problem (in Japanese),
March 8 2016,
23th Numazu conference,
March 7 -- March 9, 2016,
Numazu College of Technology, Shizuoka, Japan.
[179]
Goo Ishikawa,
Leibniz complexity of Nash functions on differentiations,
9th September 2015,
Geometric Singularity Theory, Polish-Japanese Singularity Theory Working Days,
7th --11th September 2015,
Banach Center, Warsaw, Poland.
[178]
Goo Ishikawa,
Tangential Mappings of Lagrangian Surfaces and Their Singularities,
Singularities in Generic Geometry and its Applications — Kobe - Kyoto 2015 —,
3--6 June, 8--10 June, Kobe, Kyoto 2015. (poster presentation).
[177]
Goo Ishikawa,
Geometry on flags of type D_n and associated singularities,
CAS Workshop, Geometry and related topics,
Institute of Mathematics, PAS, Poland,
24 March 2015.
[176]
Goo Ishikawa,
Neutral conformal metrics and singularities related to null curves,
Numadu, 9 March 2015.
[175]
Goo Ishikawa,
Singularities of Tangent Surfaces and Generalised Frontals,
Real Singularities and Applications,
Centre international de rencontres math{\' e}matiques
Luminy, Marseille, France,
17th February 2015.
[174]
Goo Ishikawa,
Affine connections and singularities of tangent surfaces to space curves,
Singularity theory of differential maps and its applications,
RIMS, Kyoto University,
December 5, 2014.
[173]
Goo Ishikawa,
Symplectic Singularities of Parametric Lagrangian Varieties,
Instytut Matematyczny PAN, Polskiej Akademii Nauk, Poland,
12 September 2014.
[172]
Goo Ishikawa,
Tangential Mappings of Lagrange Surfaces and their Singularities,
Faculty of Mathematics and Information Science,
Warsaw University of Technology,
8 September 2014.
[171]
Goo Ishikawa,
Singularities of Tangent Surfaces to Space Curves and Related Topics,
Center for Advanced Studies, Warsaw University of Technology, Warsaw, Poland,
3rd September 2014.
[170]
Goo Ishikawa, More trial to triality in D4-geometry from singularity theory,
March 7, 2014,
Numadu, Japan.
[169]
Goo Ishikawa, Yumiko Kitagawa, Wataru Yukuno,
Singular path duality for Cartan distributions from geometric control theory (in Japanese),
24 September 2013, Autumn Meeting 2013 of Mathematical Society of Japan,
September 24--27, 2013,
Ehime University, Ehime Japan.
[168]
Goo Ishikawa,
The D4-triality and
singularities of tangent surfaces,
6 September 2013,
Singularities in geometry and applications III,
2 September -- 6 September 2013,
The International Centre for Mathematical Sciences (ICMS),
Edinburgh, Scotland, UK.
[167]
Goo Ishikawa,
Singular path duality
for Cartan distributions
from geometric control theory,
28 August 2013,
Geometric Singularity Theory,
8th Polish-Japanese Singularity Theory Working Days,
24 August 2013 -- 31 August 2013,
The Banach Center, IMPAN, Warsaw, Poland
[166]
Goo Ishikawa,
The Work of S. Janeczko and
History of Polish-Japanese
Singularity Theory Working Days,
26 August 2013,
Geometric Singularity Theory,
8th Polish-Japanese Singularity Theory Working Days,
24 August 2013 -- 31 August 2013,
The Banach Center, IMPAN, Warsaw, Poland
[165]
Goo Ishikawa,
Singularities of Tangent Surfaces in Cartan’s Split G2-geometry,
August 30, 2012,
The V-th International Conference of Differential Geometry and Dynamical Systems
(DGDS-2012),
29 August -- 2 September 2012, Mangalia, Romania,
[164]
Goo Ishikawa, Shyuichi Izumiya’s mathematical works,
26 July, 2012,
The 12th International Workshop on Real and Complex Singularities,
July 23-- July 27, 2012,
Universidade de Sao Paulo (ICMC-USP), Sao Carlos, Brazil.
[163]
Goo Ishikawa, Tangent varieties and openings of map-germs,
18 June, 2012,
An international workshop in Singularity Theory, its Applications and Future Prospects
celebrating jubilees of Bill Bruce and Terry Wall,
18-22 June 2012,
Liverpool, UK.
[162]
Goo Ishikawa,
Singularities of tangent surfaces in G2-geometric structures,
June 2, 2012,
Singularities and Geometric Structures,
May 30 -- June 2, 2012,
Lifelong Learning Center of Nagano City, Nagano, Japan.
[161]
Goo Ishikawa,
Openings of stable unfoldings,
March 3, 2012,
AMS Sectional Meeting, Special Session on
Singularities, Stratifications and Their Applications,
March 3 -- 4, 2012,
University of Hawaii at Manoa, Honolulu, HI, USA.
[160]
Goo Ishikawa,
Openings of stable unfoldings,
2 Dec. 2011,
RIMS workshop,
Singularity theory, geometry and topology,
29 Nov. -- 2 Dec. 2011
RIMS, Kyoto, Japan.
[159]
Goo Ishikawa,
Openings of stable unfoldings,
24 Nov. 2011,
The 4th Japanese-Australian Workshop on Real and Complex Singularities,
22--25 Nove. 2011,
Kobe Satellite of Hyogo University of Teacher Education, Kobe, Japan.
[158]
Goo Ishikawa,
Singularities of Tangent Varieties and Differential Systems,
3rd June, 2011
Singularity Theory and its Applications
from 31st May to 3rd June, 2011,
Academic Hall, Oita National College of Technology, Oita, Japan.
[157]
Goo Ishikawa,
Singularities of Tangent Varieties to Curves and Surfaces,
18th May 2011.
Workshop on Singularities in Geometry and Applications,
from 15th May to 21th May, 2011.
Stefan Banach International Mathematical Center, B¥c{e}dlewo, Poland.
[156]
Goo Ishikawa,
Deformations and stability of singular Legendre varieties,
21st January 2011.
Contact Geometry, Singularities and Differential Equations,
from 21st January to 24th January, 2011.
Shyokuin Kaikan "Kamogawa", Kyoto Japan
[155]
Goo Ishikawa,
Classifications of Singularities of Mappings, Dualities and Applications.
4th December 2010.
9th Oka Symposium, Nara Women's Univ., Nara, Japan. 4th December 2010 --- 5th December 2010.
[154]
Goo Ishikawa,
Basic topics on tropical geometry and singularities.
3rd December 2010.
Geometry on Real Closed Field
and its Application to Singularity Theory,
RIMS, Kyoto University, Japan,
30th November 2010 --- 3rd December 2010.
[153]
Goo Ishikawa,
Geometry and Singularity of Framed Curves in Space Forms
and Projective Duality,
August 28, 2010,
in Differential Geometry and its Applications,
Brno, Czech Republic, August 27 - 31, 2010.
[152]
Goo Ishikawa,
Singularities of Framed Curves,
Differential Systems
and Projective Duality,
28 July 2010,
in 11th International Workshop on Real and Complex Singularities,
Celebrating the 60th birthdays of
DAVID MOND,
ICMC-USP, Sao Carlos, Brazil, 26th to 30th of July, 2010.
[151]
Goo Ishikawa,
Singularities of Framed Curves,
Differential Systems
and Projective Structures,
2 July 2010,
Singularity Seminar, Department of Mathematics, Hokkaido University, Sapporo, Japan.
[150]
Goo Ishikawa,
Generic bifurcations of framed curves in a space form and their envelopes,
27 January 2010,
Conatact structures, singularities, differential equations, 26--29 January 2010,
Toyako caluture center, Toya, Japan.
[149]
Goo Ishikawa,
Introduction to Tropical Geometry,
20 January 2010, Kobe Workshop on Singularities, 20--21 January 2010,
Kobe Satellite of Hyogo University of Teacher Education, Kobe, Japan.
[148]
Goo Ishikawa,
The Viewpoint of Real Algebraic Geometry and Recent Topics,
17 November, 2009, Colloquium talk, Hiroshima University,
Hiroshima, Japan.
[147]
Goo Ishikawa,
Generic geometry and singularities of curves on surfaces,
22 October, 2009,
Geometry Seminar,
University of Durham, England, UK,
[146]
Goo Ishikawa,
Symplectic Invariants of Parametric Singularities,
16 September, 2009,
3rd Australian-Japanese Workshop, Real and Complex Singularities,
University of Sydney, Australia,
(15--18 September, 2009).
[145]
Goo Ishikawa,
Singularity problems
in sub-Riemannian and sub-Finsler geometry,
The 44-th Symposium on Finsler Geometry
Tokai University, Sapporo Campus, Maltimedia Hall, Sapporo, Japan.
9 September 2009.
[144] Goo Ishikawa,
Symplectic Invariants of Parametric Singularities
Geometric Singularity Theory
14 July, 2009.
7th Polish-Japanese Singularity Theory Working Days,
Kazimierz Dolny, Poland,
13--19 July, 2009.
[143] Goo Ishikawa,
Geometry of surfaces with boundaries from singularity viewpoint,
School on Generic Singularities in Geometry,
Pre-workshop of 7th Polish-Japanese Singularity Theory Working Days,
Banach Center, IM-PAN, Warsaw, Poland,
10 July, 2009.
[142]
Goo Ishikawa,
Singularity Geometry of Surfaces with Boundaries and Legendre Duality,
March 25 2009,
1st Workshop on Singularities in Generic Geometry and Applications,
Valencia, Spain, March 23--27, 2009.
[141]
Goo Ishikawa,
Singularity Geometry and Topology via Legendre Duality,
18 February 2009,
Colloquium talk, Department of Mathematics, Hokkaido University
[140]
Goo Ishikawa,
Topological view --- A talk on soft geometry,
24 January, 2009. "Topological New Science",
The civic lecture for COE project.
[139]
Goo Ishikawa,
Singularity Geometry of
Legendre Surfaces with Boundaries,
29 January 2009,
"Contact Structures, Singularities,
Differential Equations and Related Topics, "
Topology Project,
Gifu Fureai Kaikan, Salamanca Hall, 27 -- 30 January, 2009.
[138]
Goo Ishikawa,
Topological view --- A talk on soft geometry,
24 January, 2009. "Topological New Science",
The civic lecture for COE project.
[137]
Goo Ishikawa,
Legendre surfaces with boundaries and projective duality,
11 December 2008,
Applications of singularity theory to differential equations and differential geometry,
2008-12-08--2008-12-11, RIMS, Japan.
[136]
Goo Ishikawa,
Symplectic invariants of Lagrangian varieties,
2 September 2008,
IM PAN, Poland
[135]
Goo Ishikawa,
Local symplectic invariants of parametric Lagrangian varieties,
26 August 2008,
Frobenius structures and singularity theory,
Bedlewo, Poland.
[134]
Goo Ishikawa,
Classification of parametric varieties in the symplectic space: Motivations, Examples and Problems,
31 July 2008,
the 10th International Workshop on Real and Compex Singularities,
Sao Carlos, Brazil.
[133]
Goo Ishikawa,
26 November 2007
Local classification of varieties
in the symplectic space,
The second Japanese-Australian Workshop on Real and Complex Singularities,
RIMS, Kyoto, Japan.
[132]
Goo Ishikawa,
13 November 2007
Local classification of varieties
in the symplectic space,
The 14th Workshop "Symplectic Geometry and Related Topics"
Gifu Economy Collage, Ohgaki, Japan.
[131]
Goo Ishikawa,
27 July 2007
Local classification of parametric Lagrangian varieties,
Internation Conference "Symplectic Geometry"
RIMS, Kyoto, Japan.
[130]
Goo Ishikawa,
9 July 2007,
Calssification problem in symplectic singularity theory,
Banach Center Symposium "Geometric Singularity Theory"
Polish-Japanese Working Days,
Sopot, Poland.
[129]
Goo Ishikawa, A differentiable structure on a mapping space quotient
and its application to the moduli problem,
Perspectives of Differential Analysis and Singularity Theory,
May 21, 2007 (Monday) - May 22, 2007 (Tuesday),
Room 4-508, Faculty of Science Building #4, Hokkaido University,
Organizer:
Shuzo IZUMI (Kinki Univ.), Goo ISHIKAWA (Hokkaido Univ.),
May 21, 2007 (Monday).
[128]
G. Ishikawa,
On Tropical Geometry,
7 March 2007,
Numadu, Japan.
[127]
G. Ishikawa,
Introduction to Tropical Geometry,
I, II, III, IV, V,
13--14 January 2007.
Spring School. Tohoku Univ., Sendai, Japan.
[126]
G. Ishikawa,
A differentiable structure on a mapping space quotient
and its application to the moduli problem.
28 Nov. 2006.
RIMS, Kyoto Japan.
[125]
G. Ishikawa,
Classification of phase singularities for complex scalar waves.
(Jointwork with J. Adachi).
8th September 2006.
The international symposium on singularity theory and its applications,
長沙理工大学
Changsha, China.
[124]
G. Ishikawa,
On the classification of planar curve singularities,
4th September 2006. 東北師範大学，
Changchun, China.
[123]
G. Ishikawa,
Zariski's moduli problem for plane branches and
the classification of Legendre curve singularities,
26 June 2006.
ICMC, USP, Sao Carlos, Brazil.
[122]
G. Ishikawa,
On quantum singularity theory,
12th April, 2006.
Singularity Seminor, Hokkaido University, Sapporo
[121]
J. Adachi, G. Ishikawa,
Classification of phase singularities for complex scalar waves.
13th --15th December 2005.
PHASE SINGULARITIES AND TOPOLOGY'' (PST05)
15th December 2005.
[120]
Goo ISHIKAWA,
Extra singularities in geometric solutions to
Monge-Amp¥`ere equations of three variables.
October 2005.
Developments of Cartan Geometry and Related Mathematical Problems,
RIMS, Kyoto, JAPAN.
[119]:
Goo ISHIKAWA,
Singularities of parametric Legendre surfaces.
Singularities of Differential Systems,
11 Octorber -- 13 October 2005,
Department of Mathematics, Hokkaido Univ.
Sapporo JAPAN.
[118]:
Goo ISHIKAWA,
Singularities of parametric plane curves and Legendre curves.
Australian-Japanese Workshop on Real and Complex Singularities,
5 September 2005 - 8 September 2005.
University of Sydney,
Australia.
[117]:
Goo ISHIKAWA,
Singularities of Legendre curves and related topics,
First South Pacific Conference on Mathematics,
Noum¥'ea, New Caledonia, 29/08-02/09, 2005.
[116]:
Goo ISHIKAWA,
The complex symplectic moduli spaces of
uni-modal parametric plane curve singularities.
Polish-Japanese Working Days V,
16 July 2005, Bukowinatatrzanska, Poland.
[115]:
Goo ISHIKAWA,
Classifying singular Legendre submanifolds and pseudo-fronts,
Symposium "Contact structure, Singularities and Related Areas"
Ohgaki, Japan. 22th January 2005.
[114]:
Goo ISHIKAWA,
Singular Legendre curves and Goursat distributions,
"Geometry in Nara -- Around Subriemannian Geometries",
Nara Women's Univ., Nara, Japan.
13th December 2004.
[113]:
Goo ISHIKAWA,
Local classification of varieties in the presence of a geometric structure,
"The Method of Algebraic Analysys in Singularity Theory",
Kagoshima Univ., Kagoshima, Japan.
9th December 2004.
[112]:
Goo ISHIKAWA,
A very easy introduction to amoebas and tropical geometry (A report on the "e-mail seminar").
29 October 2004.
Singularity Theory Working Days in Hakodate,
27 October -- 30 October 2004, Hakodate, Japan.
[111]:
Goo ISHIKAWA,
Parametric coisotropic varieties and related topics,
(Joint work with S. Janeczko).
Banach Center Symposium,
Goemtric Singularity Theory,
Polish-Japanese Singularity Theory Working Days IV,
Bedlewo, Poland. 4th September 2004.
[110]:
Goo ISHIKAWA,
Singularities of affine spheres and their duals,
9th international Confenrece on Differential Geometry and its Applications,
August 30 - September 3, 2004,
Prague, Czech Republic. 31th August, 2004.
[109]:
Goo ISHIKAWA,
Singular Legendre surves and Goursat systems,
International Conference on Differential Equations and Dynamical Systems,
Suzdal, July' 05 - 10, 2004, Russia. 7th July 2004.
[108]:
Goo ISHIKAWA,
Singularities of affine spheres and pseudo-spheres (II),
The First Chinese-Japanese Singularity Theory Workshop,
Northeast Normal University, Changchun, China. 2nd June 2004.
[107]:
Goo ISHIKAWA,
Singularities of affine spheres and pseudo-spheres (I),
The First Chinese-Japanese Singularity Theory Workshop,
Northeast Normal University, Changchun, China. 1st June 2004.
[106]:
Goo ISHIKAWA,
Singular Legendre curves and Goursat distributions,
Symposium "Contact structure, Singularities and Related Areas"
Matsumoto, Japan. January 2004.
特異ルジャンドル曲線とグルサ系，
シンポジウム「接触構造，特異点と関連分野」，
松本市中央公民館(Mウィング)，松本，日本．
[105]:
２００３年１１月
Motivic integration and non-holonomic geometry（e-mail 勉強会報告），
数理解析研究所研究集会「特異点論における新しい方法と対象」 ，
京都大学数理解析研究所，京都，日本．
[104]:
２００３年１１月
Moduli spaces of plane curve singularities,
シンプレクティック幾何と関連分野，
岐阜経済大，大垣，日本．
[103]:
２００３年９月
Moduli spaces of Lagrange varieties,
3rd Japanese-Polish working days,
北大，日本．
[102]:
２００３年５月
Tangentially degenerate fronts and their singularities,
Workshop of Webs and Projective Differentiable Geometry,
Matue, Shimane, Japan.
[101]:
２００３年３月
Moduli space of singular curves in the symplectic plane, ¥¥
Classifying singular Legendre curves,
by contactomorphisms.
日本数学会年会，東大，日本．
[100]:
２００３年１月
特異ルジャンドル曲線の分類問題，
研究集会「接触構造，特異点と関連問題」
呉市きんろうプラザ大会議室，呉，日本．
[99]:
２００２年１２月
Classification problems of Lagrangian varieties,
Topology of Real and Complex Singularities II,
鹿児島大学理学部．
[98]:
２００２年９月
Symplectic singularities of isotropic mappings,
Polish-Japanese Singularity Theory Working Days II,
Banach Center Symposium,
Bedlewo, Poland.
[97]:
２００２年６月２４日，
Perturbations of caustics and fronts,
Geometry and Topology of Caustics, Caustics'02,
Banach Center Symposium,
Warsaw, Poland.
[96]:
２００１年１２月，
ラグランジュ・ルジャンドル特異点論の基礎，
研究集会「光学の数理解析」，
お茶の水女子大学，東京．
[95]:
２００１年１１月２７日，
Singularities of curves in the symplectic plane,
研究集会「シンプレクティック幾何学とその周辺」，
岐阜経済大学．
[94]:
２００１年９月２２日，
Lagrangian liftings of parametrized varieties,
Polish-Japanese Singularity Theory Working Days,
Banach Center Symposium,
Bedlewo, Poland.
[93]:
２００１年６月９日，
Topological bifurcation of developable surfaces to space curves,
国際特異点論研究集会，
東北師範大学，長春，中国．
[92]:
２００１年３月９日，
量子化条件とラグランジュ特異点の特性類，
第９回沼津研究会，
沼津高専．
[91]:
２００１年１月２４日，
旗多様体上のカノニカル分布に対する積分曲線の
特異性と接可展面の位相的分岐，
シンポジウム「接触構造，特異点，微分方程式」，
福岡大学．
[90]:
２０００年１１月１５日，
Singularities of multi-valued functions and Grassmann
geometry,
Symplectic 幾何とその周辺，
秋田大学工学部，
[89]:
２０００年１１月９日，
Perturbations of Caustics and Fronts:
An Application of Singularity Theory
and Differential Analysis,
実特異点論研究集会，
横浜シンポジア，
横浜．
[88]:
２０００年９月２７日，
Versality theorem for singular
Legendre immersions,
Newton Institute,
The University of Cambridge,
ケンブリッジ，イギリス．
[87]:
２０００年９月１７日，
The non-linear version of
geometric subgroups and subspaces,
Newton Institute,
The University of Cambridge,
ケンブリッジ，イギリス．
[86]:
２０００年６月２７日，
Versality of isotropic mappings in poly-symplectic
geometry,
Institute of Mathematics,
Warsaw University of Technology,
ワルシャワ，ポーランド．
[85]:
２０００年６月２０日，
Simple stable projections of Lagrange varieites ---
Joint work with Ilia Bogaevskii,
Institute of Mathematics,
Warsaw University of Technology,
ワルシャワ，ポーランド．
[84]:
２０００年５月２４日，
Singularities of Grassmannian fornts,
幾何学コロキウム，
北海道大学．
[83]:
２０００年３月２８日，
ラグランジュ・ルジャンドル特異点をめぐって ---
２０００年のカタストロフ理論，
日本数学会年会企画特別講演，
早稲田大学．
[82]:
２０００年３月４日，
ヒルベルト第１６問題について，
香川大学セミナー，
香川大学．
[81]:
２０００年１月１０日，
サブリーマン波面，コースティックとカルノー・カラテオドリ球面の特異性，
「測地線の幾何学」
熊本大学．
[80]:
１９９９年１２月２０日，
Recent Results on Developable Submanifolds: Examples and
Classifications,
The International Conference 「100 years after Sophis Lie 」
奈良女子大学．
[79]:
１９９９年１０月２８日，
特異ラグランジュ多様体の単純射影(イリア・ボガエフスキー氏との共同研究)，
「シンプレクティック幾何学とその周辺」，
岐阜経済大学．
[78]:
１９９９年９月９日，
Non-linear version of Damon's theory of
geometric subgroups and subspaces,
研究会「いろいろなカテゴリーでの多様体のトポロジーと特異点」
和歌山大学．
[77]:
１９９９年８月４日，
実射影空間内の可展超曲面と等質空間，
第４６回幾何学シンポジウム，
東京大学大学院数理科学研究科．
[76]:
１９９９年６月２４日，
Stable projections of open Whitney umbrellas,
Workshop on Singularity Theory,
Warwick 大学，England, U.K. (イギリス)．
[75]:
１９９９年６月１日，
Several Questions on Singularities: Theory and Applications,
短期共同研究会「特異点の研究」
京都大学数理解析研究所．
[74]:
１９９９年２月，
応用特異点論の基礎，
「Encounter with Mathematics」，
中央大学．
[73]:
１９９８年１２月２３日，
Developable hypersurfaces and homogeneous spaces in a real
projective space,
シンポジウム「リー群と幾何学」，
横浜市立大学．
[72]:
１９９８年１１月２５日，
ラグランジュ特異点論における確定性，横断性，安定性，
研究集会「シンプレクティック幾何学とその周辺」
秋田大学．
[71]:
１９９８年１０月２９日，
Singularities of tangent developables to space curves,
Workshop on Singularity Theory for
Shape Interrogation,
会津大学．
[70]:
１９９８年９月３０日，
接触多様体内のルジャンドル特異はめ込みの安定性，
１９９８年９月３０日，
ラグランジュ安定写像とルジャンドル安定写像の確定性，
１９９８年１０月１日，
写像に沿ったベクトル場によるリー微分，普遍リー微分とその応用，
日本数学会１９９８年度秋季総合分科会，
大阪大学．
[69]:
１９９８年９月，
Determinacy, Transversality and Lagrange stability,
Arnold Seminar of Moscow State Univ.,
Moscow, Russia.
[68]:
１９９８年９月，
Developable hypersurfaces and homogeneous spaces in a real
projective space,
The pre-conference of 100 years after Sophis Lie,
Kazan, Russia.
[67]:
１９９８年７月３日，
実射影空間内の可展超曲面と等質空間，
研究集会「等質構造の部分多様体的研究」，
京都大学数理解析研究所．
[66]:
１９９８年６月，
Stable projections of open Whitney umbrellas,
「Caustic '98」,
Banach Center,
Warsaw, Poland.
[65]:
１９９７年１２月，
sub-Riemannian geometry における波面，焦面，球面，最小跡の特異性，
関西微分解析セミナー，
近畿大学．
[64]:
１９９７年１２月，
tangent developable にまつわる etc. --
射影双対，Legendre 特異点，可微分代数，寡項式，Kuiper-Kuo 定理，等質空間
そして Cayley 数学，
関西微分解析セミナー，
近畿大学．
[63]:
１９９７年１２月，
実射影空間の可展超曲面と等質空間，
熊本大学理学部談話会，
熊本．
[62]:
１９９７年１２月，
sub-Riemannian geometry における波面，焦面，球面，最小跡の特異性，
熊本大学教育学部幾何セミナー，熊本．
[61]:
１９９７年１０月，
Real projective varities with degenerate duals,
「Workshop on Real and Complex Singularities in KAGOSHIMA」,
鹿児島大学．
[60]:
１９９７年９月３０日，
実射影空間の可展開超曲面と実代数等質空間，
(トポロジー分科会),
１９９７年１０月３日，
実射影空間の可展開超曲面と実代数等質空間，
(幾何学分科会)，
日本数学会１９９７年度秋季総合分科会，
東京大学．
[59]:
１９９７年９月，
Real developable varieties and real homogeneous spaces,
「Singularities and Related Topics」,
東北師範大学，
長春，
中国．
[58]:
１９９７年１月、
サブリーマン幾何への特異点論の応用の可能性(Agrachevたちの仕事)、
科研費研究会「Carnot-Caratheodory 計量とその周辺」
(Sub-Riemannian geometry と制御理論の幾何学的研究)、
金沢大学工学部．
[57]:
１９９７年１月、
サブリーマン幾何への特異点論の応用の可能性、
短期共同研究 「実特異点のトポロジーとその関連話題」、
京都大学数理解析研究所．
[56]:
１９９６年１１月、
シンプレクティック幾何に現われる特異点とその安定性について、
研究集会「Poisson Geometry and Symplectic Geometry」、
岐阜経済大学．
[55]:
１９９６年８月、
Topological classification of the tangent developables,
TERRY WALL'S 60TH BIRTHDAY MEETING, LIVERPOOL,
AUGUST 19TH-24TH, 1996、
総合講演、
リヴァプール大学、
イギリス．
[54]:
１９９６年７月、
Topology of plane trigonometric curves and
closures of real pseudo-line arrangements,
Workshop on Real and Complex Singularities,
総合講演、
サンパウロ大学サンカルロス数理科学研究所、
ブラジル．
[53]:
１９９６年１月、
Singularity theory of frontal mappings and its applications,
シンポジウム $¥lceil$ 接触幾何と関連分野 $¥rfloor$ 、
北海道大理学研究科．
[52]:
１９９６年１月、
Topology of parametric plane curves -- Analogy to
Hilbert's 16th problem,
短期共同研究 $¥lceil$ 可微分写像の特異点論：トポロジーと応用、
京都大学数理解析研究所．
[51]:
１９９５年９月、
空間曲線の可展開面の位相型、
日本数学会秋季総合分科会、
東北大．
[50]:
１９９５年８月２９日、
曲線の可展開面の位相的分類、
研究集会「特異点論の発展と展望」、
高知大．
[49]:
１９９５年７月、
シンプレクティック
幾何における特異点論、
第４２回トポロジーシンポジウム、
弘前大理学部．
[48]:
１９９５年６月、
アフィン曲線のトポロジー --- 可展開面のはなし、
北海道幾何学コロキウム、
北海道大理学部．
[47]:
１９９５年３月、
Symplectic and Lagrange singularities of open Whitney umbrellas,
短期共同研究集会、
京都大学数理解析研究所．
[46]:
１９９４年１１月、
Symplectic and Lagrange singularities of open Whitney umbrellas,
数学科コロキュウム、
サザンプトン大学、ＵＫ．
[45]:
１９９４年１１月、
Singularities of developable surfaces of curves,
純粋数学科コロキュウム、
リヴァプール大学、ＵＫ．
[44]:
１９９４年１０月、
Symplectic and Lagrange singularities of open Whitney umbrellas,
純粋数学科特異点セミナー、
リヴァプール大学、ＵＫ．
[43]:
１９９４年１月、
ルジャンドル特異点論とその応用，
接触幾何学と関連分野，
大阪大学理学部．
[42]:
１９９３年１０月、
Singularities of isotropic mappings and front mappings,
Banach Center Symposium on singularities and differential equations,
ポーランド ワルシャワ バナッハ研究所．
[41]:
１９９３年９月、
Singularities of developables of curves,
Banach Center Symposium on singularities and differential equations,
ポーランド ワルシャワ バナッハ研究所．
[40]:
１９９３年３月、
Determinacy of developables relatively to the osculation type,
Workshop on Topology and Geometry,
ヴェトナム ハノイ数学研究所．
[39]:
１９９３年１月、
ルジャンドル特異点論の一般化をめざして，
接触幾何学と関連分野，
北海道大学理学部．
[38]:
１９９２年８月、
Maslov classes appearing in symplectic reduction,
研究集会 $¥lceil$ Microlocal Geometry $¥rfloor$ ，
京都大学数理解析研究所．
[37]:
１９９２年６月、
アイソトロピック写像芽 ${¥bf R}^2,0 ¥to {¥bf C}^2,0$ の分類の試み，
短期共同研究集会「実特異点と実代数幾何」，
京都大学数理解析研究所．
[36]:
１９９２年１月、
Singular Lagrange and Legendre varieties,
福井芦原トポロジー小研究会、
福井．
[35]:
１９９１年１２月、
Invariants of singular Lagrange surfaces, シンポジウム $¥lceil$ 特異点の研究 $¥rfloor$ 、
名古屋大学．
[34]:
１９９１年１０月、
曲線の可展開面の特異点について、日本数学会総合分科会、北大理．
[33]:
１９９１年８月、
ラグランジュ、ルジャンドル多様体の分類と不変量、
微分幾何鹿沢セミナー、東工大鹿沢合宿所．
[32]:
１９９１年３月、
Developable of a curve and its determinacy
relative to osculation type,
短期共同研究 $¥lceil$ 実特異点の研究 $¥rfloor$
数理解析研究所．
[31]:
１９９１年３月、
曲線の射影幾何に現れる特異点について、近畿大学理工学部
コロキウム．
[30]:
１９９０年１２月、
Maslov class of a singular Lagrangian varieties,
古典力学、量子力学とトポロジー、賢島研修センター，
三重県．
[29]:
１９９０年８月、
Construction of Lagrangian varieties,
特異点シンポジウム、東京工業大学．
[28]:
１９８９年１０月、
A differentiable algebra appearing in symplectic geometry,
研究集会 $¥lceil$ 微分解析と微分位相幾何 $¥rfloor$ 、
数理解析研究所，
京都大学．
[27]:
１９８９年８月、
Singular Lagrange varieties,
第３６回幾何学シンポジウム、
東北大教養部．
[26]:
１９８９年１月，
Lagrange 安定性，相対 de Rham コホモロジーと Poisson 構造，
「シンプレクティック多様体のトポロジー」，
京都府立ゼミナールハウス，
京都．
[25]:
１９８９年１月、
Lagrange ヴァライティー $¥cdot$ 相対 de Rham コホモロジーと
Poisson 構造、
シンポジウム
$¥lceil$ 特異点論とその応用 $¥rfloor$ 、
北海道大理学部．
[24]:
１９８８年１２月、
１階常微分方程式と積分図式、
日本数学会北海道分科会、
北海道大理学部．
[23]:
１９８８年１０月、
Topics on Hilbert's 16th problem,
研究集会 $¥lceil$ 実代数幾何 $¥rfloor$ 、
数理解析研究所．
[22]:
１９８７年１１月、
Parametrization of a singular Lagrange variety,
研究集会 $¥lceil$ 特異点の研究 $¥rfloor$ 、
数理解析研究所．
[21]:
１９８７年１０月，
Singularity of an isotropic mapping,
「実幾何学における諸方法」，
近畿大学．
[20]:
１９８７年１０月、
特異ラグランジュ多様体のパラメーター付け、
日本数学会秋季総合分科会、
京都大理学部．
[19]:
１９８７年１月、
ラグランジュ
特異点とルジャンドル特異点、
シンポジウム $¥lceil$
シンプレクティック
多様体の
トポロジー $¥rfloor$ 、
京都府ゼミナールハウス．
[18]:
１９８６年１１月、
Topics on real enumerative geometry,
短期共同研究集会 $¥lceil$ $C^¥infty$-写像の特異点と接触幾何学 $¥rfloor$ 、
数理解析研究所．
[17]:
１９８６年９月、
実平面曲線の特異点の摂動について、
日本数学会秋季総合分科会、
福井大．
[16]:
１９８５年１２月、
研究集会 $¥lceil$ 複素解析的特異点と可換環 $¥rfloor$ 、
${¥bf P}^n¥times{¥bf P}^1$の実超曲面のトポロジー、
数理解析研究所．
[15]:
１９８５年９月、
臨界点の個数が最小の実有理関数、
日本数学会秋季総合分科会、
富山大．
[14]:
１９８５年９月、
The number of critical points of real rational functions,
Colloque ¥lq¥lq G¥' eom¥' etrie Alg¥' ebrique R¥' eelle",
Luminy大（マルセイユ）．
[13]:
１９８５年７月、
実有理関数の臨界点とHilbert第１６問題、
第３３回全日本トポロジーシンポジウム、
信州大．
[12]:
１９８５年４月、
実平面代数曲線束に現れる特異点の個数、
日本数学会年会、
都立大教養部．
[11]:
１９８５年２月、
実有理関数の臨界点の個数、
特異点シンポジウム、
伊豆大川．
[10]:
１９８４年１１月、
実平面代数曲線束に現れる特異点の個数、
研究集会 $¥lceil$ $C^¥infty$-写像とその特異点 $¥rfloor$ 、
数理解析研究所．
[9]:
１９８４年４月、
$C^¥infty$写像芽の$C^¥infty$無限確定性、
日本数学会年会、
大阪大工学部．
[8]:
１９８３年１２月、
可微分写像芽の$C^¥infty$無限確定性、
微分可能多様体シンポジウム、
兵庫教育大．
[7]:
１９８３年９月、
可微分写像芽の位相確定性、
日本数学会秋季総合分科会、
早稲田大理工学部．
[6]:
１９８３年４月、
写像の特異性に従う関数族について、
日本数学会年会、
広島大理学部．
[5]:
１９８２年１２月、
実代数曲線のトポロジー、
微分可能多様体シンポジウム、
蒲郡．
[4]:
１９８２年１０月、
可微分写像芽の位相確定性、
研究集会 $¥lceil$ $C^¥infty$-写像と関連分野 $¥rfloor$ 、
数理解析研究所．
[3]:
１９８２年９月、
A remark on topological finite determinacy,
日本数学会秋季総合分科会、
三重大．
[2]:
１９８１年１２月、
写像の特異性とそれに従う関数族、
微分可能多様体シンポジウム、
舞鶴高専．
[1]:
１９８０年８月、
$C^2$-安定性について、
研究集会 $¥lceil$ $C^¥infty$-写像と特異集合 $¥rfloor$ 、
数理解析研究所．
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Goo Ishikawa