Research Activities

Preprints arXiv / Front for the arXiv

(with Kazuki Kanai, Aiichi Yamasaki) Norm one tori and Hasse norm principle, III: Degree 16 case, 74 pages. arXiv:2404.01362 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Aiichi Yamasaki) Rationality problem for norm one tori for $A_5$ and $PSL_2(F_8)$ extensions, 23 pages. arXiv:2309.16187 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Kazuki Kanai, Aiichi Yamasaki) Hasse norm principle for $M_{11}$ and $J_1$ extensions, 17 pages. arXiv:2210.09119 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Aiichi Yamasaki) Birational classification for algebraic tori, 175 pages. arXiv:2112.02280 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Ming-chang Kang, Aiichi Yamasaki) An application of cohomological invariants, 11 pages. arXiv:1903.03750

Papers MathSciNet / zbMATH / Algorithm [ Niigata | Kyoto | KURENAI 1 2 3 4 5 6 ]

(with Hidetaka Kitayama) Rationality problem of two-dimensional quasi-monomial group actions,
Transformation Groups 29 (2024/2-9) 1029-1064. Springer Preprint version: arXiv:2012.12046
(with Aiichi Yamasaki) Rationality problem for norm one tori for dihedral extensions,
Journal of Algebra 640 (2024/2) 368-384. ScienceDirect Preprint version: arXiv:2302.06231
(with Ming-chang Kang, Aiichi Yamasaki) Multiplicative Invariant Fields of Dimension ≤ 6,
Memoirs of the American Mathematical Society 283 (2023/3), no. 1403, vi+137 pp. AMS Bookstore Preprint version: arXiv:1609.04142 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Kazuki Kanai, Aiichi Yamasaki) Norm one tori and Hasse norm principle, II: Degree 12 case,
Journal of Number Theory 244 (2023/3) 84-110. ScienceDirect Extended version: arXiv:2003.08253 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Kazuki Kanai) Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods,
Finite Fields and their Applications 84 (2022/12) Paper No. 102101, 26 pp. ScienceDirect Extended version: arXiv:2105.14872
(with Kazuki Kanai, Aiichi Yamasaki) Norm one tori and Hasse norm principle,
Mathematics of Computation 91 (2022/9) 2431-2458. AMS Extended version: arXiv:1910.01469 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Ming-chang Kang, Hidetaka Kitayama, Aiichi Yamasaki) A two-dimensional rationality problem and intersections of two quadrics,
Manuscripta Mathematica 168 (2022/5-7) 423-437. Springer Preprint version: arXiv:1801.06616
(with Aiichi Yamasaki) Rationality problem for norm one tori,
Israel Journal of Mathematics 241 (2021/3), no. 2, 849-867. Springer Extended version: arXiv:1811.01676 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Masakazu Koshiba) On Lecacheux's family of quintic polynomials,
Proceedings of the Japan Academy, Series A 97 (2021/1), no. 1, 1-6. Project Euclid Extended version: arXiv:2003.13458
(with Hidetaka Kitayama) Three-dimensional purely quasimonomial actions,
Kyoto Journal of Mathematics 60 (2020/4), no. 1, 335-377. Project Euclid Preprint version: arXiv:1501.03558
(with Sumito Hasegawa, Aiichi Yamasaki) Rationality problem for norm one tori in small dimensions,
Mathematics of Computation 89 (2020/3), no. 322, 923-940. AMS Extended version: arXiv:1811.02145 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Ming-chang Kang, Aiichi Yamasaki) Degree three unramified cohomology groups and Noether's problem for groups of order 243,
Journal of Algebra 544 (2020/2), 262-301. ScienceDirect Extended version: arXiv:1710.01958 / Algorithm [ Niigata | Kyoto | KURENAI ]
(with Ming-chang Kang, Aiichi Yamasaki) Rationality problems for relation modules of dihedral groups,
Journal of Algebra 530 (2019/7), 368-401. ScienceDirect Preprint version: arXiv:1503.04543 Old version: Class numbers and algebraic tori. arXiv:1312.6738
(with Aiichi Yamasaki) Rationality problem for algebraic tori,
Memoirs of the American Mathematical Society 248 (2017/7), no. 1176, v+215 pp. AMS Bookstore Preprint version: arXiv:1210.4525 / Algorithm [ Niigata | Kyoto | KURENAI ]
Complete solutions to a family of Thue equations of degree 12,
Journal de Théorie des Nombres de Bordeaux 29 (2017/7), 549-568. JTNB
(with Ming-chang Kang, Aiichi Yamasaki) Degree three unramified cohomology groups,
Journal of Algebra 458 (2016/7), 120-133. ScienceDirect Preprint version: arXiv:1503.08375
Birational classification of fields of invariants for groups of order 128,
Journal of Algebra 445 (2016/1), 394-432. ScienceDirect Preprint version: arXiv:1404.0308
(with Huah Chu, Shou-Jen Hu, Ming-chang Kang) Noether's problem for groups of order 243,
Journal of Algebra 442 (2015/11), 233-259. ScienceDirect Preprint version: arXiv:1403.0318
On Noether's problem for cyclic groups of prime order,
Proceedings of the Japan Academy, Series A 91 (2015/3), no. 3, 39-44. Project Euclid Extended version: arXiv:1402.3678
On the simplest quartic fields and related Thue equations,
Computer Mathematics, Springer, 67-85, 2014/10. Springer Preprint version: arXiv:1004.1960
(with Ming-chang Kang, Hidetaka Kitayama) Quasi-monomial actions and some 4-dimensional rationality problems,
Journal of Algebra 403 (2014/2), 363-400. ScienceDirect Preprint version: arXiv:1201.1332
(with Ming-chang Kang, Boris E. Kunyavskii) Noether's problem and unramified Brauer groups,
Asian Journal of Mathematics 17 (2013/12), no. 4, 689-714. International Press Old version: Unramified Brauer groups for groups of order p^5 arXiv:1109.2966
On the simplest sextic fields and related Thue equations,
Functiones et Approximatio, Commentarii Mathematici 47 (2012/9), no. 1, 35-49. Project Euclid
On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields,
Journal of Number Theory 131 (2011/11), no. 11, 2135-2150. ScienceDirect
(with Hidetaka Kitayama, Aiichi Yamasaki) Rationality problem of three-dimensional monomial group actions,
Journal of Algebra 341 (2011/9), no. 1, 45-108. ScienceDirect
(with Ming-chang Kang) Twisted symmetric group actions,
Pacific Journal of Mathematics 248 (2010/12), no. 2, 285-304. Pacific J. Math. Preprint version: arXiv:0812.4807
(with Katsuya Miyake) On the field intersection problem of solvable quintic generic polynomials,
International Journal of Number Theory 6 (2010/8), no. 5, 1047-1081. World Scientific Preprint version: arXiv:0804.4875
(with Katsuya Miyake) A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations,
Interdisciplinary Information Sciences 16 (2010/3), no. 1, 45-54.
Special Section: Japan-Korea Joint Seminar on Number Theory and Related Topics 2008. J-STAGE
(with Katsuya Miyake) On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation,
Commentarii Mathematici Universitatis Sancti Pauli 58 (2009/7), no. 1, 51-86. Rikkyo Roots Preprint version: arXiv:0812.4807
(with Katsuya Miyake) A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation,
Number theory and applications, 65-104, Proceedings of the International Conferences on Number Theory and Cryptography
held in Allahabad, December 2006 and February 2007. Edited by S. D. Adhikari and B. Ramakrishnan.
Hindustan Book Agency, New Delhi, 2009/3. AMS Springer Preprint version: arXiv:0710.0287
(with Ming-chang Kang) A rationality problem of some Cremona transformation,
Proceedings of the Japan Academy, Series A 84 (2008/10), no. 8, 133-137. Project Euclid
(with Yuichi Rikuna) Rationality problem of three-dimensional purely monomial group actions: the last case,
Mathematics of Computation 77 (2008/7), no. 263, 1823-1829. AMS
(with Ki-ichiro Hashimoto and Yuichi Rikuna) Noether's problem and Q-generic polynomials for the normalizer of the 8-cycle in S₈ and its subgroups,
Mathematics of Computation 77 (2008/4), no. 262, 1153-1183. AMS
(with Katsuya Miyake) Tschirnhausen transformation of a cubic generic polynomial and a 2-dimensional involutive Cremona transformation,
Proceedings of the Japan Academy, Series A 83 (2007/3), no. 3, 21-26. Project Euclid
Explicit lifts of quintic Jacobi sums and period polynomials for F_q,
Proceedings of the Japan Academy, Series A 82 (2006/9), no. 7, 87-92. Project Euclid
(with Ki-ichiro Hashimoto) Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations,
Mathematics of Computation 74 (2005/7), no. 251, 1519-1530. AMS
(with Ki-ichiro Hashimoto) Geometric generalization of Gaussian period relations with application to Noether's problem for meta-cyclic groups,
Tokyo Journal of Mathematics 28 (2005/6), no. 1, 13-32. Project Euclid
Noether's problem for some meta-abelian groups of small degree,
Proceedings of the Japan Academy, Series A 81 (2005/1), no. 1, 1-6. Project Euclid
Multiplicative quadratic forms on algebraic varieties,
Proceedings of the Japan Academy, Series A 79 (2003/4), no. 4, 71-75. Project Euclid

Ph.D. Dissertation

Multiplicative quadratic forms on algebraic varieties and Noether's problem for meta-abelian groups,
Waseda University, March 2005. Waseda University

Refereed Articles & Surveys

Noether's problem and rationality problem for multiplicative invariant fields: a survey,
Algebraic number theory and related topics 2016, 29-53, RIMS Kôkyûroku Bessatsu B77,
Res. Inst. Math. Sci. (RIMS), Kyoto, (2020/4). Kyoto / RIMS
Rationality problem for quasi-monomial actions,
Algebraic number theory and related topics 2012, 203-227, RIMS Kôkyûroku Bessatsu B51,
Res. Inst. Math. Sci. (RIMS), Kyoto, (2014/10). Kyoto / RIMS
(with Katsuya Miyake) Some Diophantine problems arising from the isomorphism problem of generic polynomials,
Number Theory: Dreaming in Dreams, 87-105, Proceedings of the 5th China-Japan Seminar.
Edited by T. Aoki, S. Kanemitsu and J. Liu, World Sci. Publ., Singapore, 2009/11. World Scientific
(with Katsuya Miyake) On the field intersection problem of generic polynomials: a survey,
Algebraic number theory and related topics 2007, 231-247, RIMS Kôkyûroku Bessatsu B12,
Res. Inst. Math. Sci. (RIMS), Kyoto, (2009/8). Kyoto / RIMS

Honors

2024 Sep.	Niigata University Outstanding Paper Award, Niigata University Niigata
2023 Aug.	Niigata University Scholarly Publishing Award, Niigata University Niigata
2021 Dec.	Niigata University Outstanding Paper Award, Niigata University Niigata
2016 Nov.	Niigata University President's Award, Niigata University Niigata
2005 Mar.	Representative of Ph.D. (D.Sc.) recipients, Waseda University

Research Grants

2024	Niigata University Outstanding Paper Award 100,000 yen Niigata
2024 - 2026	Grant-in-Aid for Scientific Research (B) 24K00519 9,230,000 yen KAKEN
2023	Niigata University Scholarly Publishing Award 100,000 yen Niigata
2021	Niigata University Outstanding Paper Award 100,000 yen Niigata
2019 - 2022	Grant-in-Aid for Scientific Research (C) 19K03418 4,290,000 yen KAKEN
2018	Niigata University Grant-in-Aid for International Conference Participation Support Project 200,000 yen
2017	Niigata University Grant-in-Aid for Scientific Research Application Support Program 700,000 yen
2016	Niigata University President's Award (Research Grant for Young Researchers) 800,000 yen Niigata
2013 - 2016	Grant-in-Aid for Scientific Research (C) 25400027 4,810,000 yen KAKEN
2010 - 2012	Grant-in-Aid for Young Scientists (B) 22740028 2,340,000 yen KAKEN
2009	Rikkyo University Special Fund for Research 500,000 yen Rikkyo
2008	Rikkyo University Special Fund for Research 500,000 yen Rikkyo
2007	Waseda University Grant for Special Research Projects (2007B-067) 450,000 yen
2006	Waseda University Grant for Special Research Projects (2006A-850) 200,000 yen
2004 - 2005	Grant-in-Aid for JSPS Fellows 04J01682 1,900,000 yen KAKEN

Research Grants (Co-Investigator)

2024 - 2027	Grant-in-Aid for Scientific Research (C) 24K06647 KAKEN
2020 - 2024	Grant-in-Aid for Scientific Research (A) 20H00115 KAKEN
2010 - 2014	Grant-in-Aid for Scientific Research (C) 22540032 KAKEN
2007 - 2008	Grant-in-Aid for Scientific Research (C) 19540057 KAKEN
2006 - 2009	Grant-in-Aid for Scientific Research (C) 18540048 KAKEN

Visits & Attendances

2024	Nov.	(2 weeks)	King's College London, the United Kingdom
2024	Nov.	(1 day)	London Number Theory Seminar, Imperial College London, the United Kingdom Web
2024	Nov.	(1 day)	Bath Arithmetic Geometry Seminar, University of Bath, the United Kingdom Google
2024	Sep.	(3 days)	The 5th International Congress on Natural Sciences with Sisterhood Universities (ICNS2024), Niigata University, Japan ICNS2024
2023	Dec.	(3 days)	Yufuin Workshop on Algebraic Geometry, Nippon Bunri University, Japan Google
2023	Dec.	(1 week)	Algebraic Number Theory and Related Topics 2023, RIMS, Kyoto University, Japan RIMS
2023	Dec.	(3 days)	Niigata Algebra Symposium, Niigata University, Japan Niigata
2023	Oct.	(1 week)	Kinosaki algebraic geometry symposium 2023, Kinosaki International Arts Center, Japan WordPress
2023	Oct.	(1 week)	International workshop on Birational Geometry, Nagoya Univeristy, Japan WordPress
2023	Sep.	(1 week)	MFO-RIMS Tandem workshop 2023 - Arithmetic Homotopy and Galois Theory, RIMS, Kyoto Univeristy, Japan AHGT IRN
2023	Sep.	(1 day)	Number theory joint seminar, Department of Mathematics, Kyoto Univeristy, Japan Kyoto
2023	Aug.	(4 days)	The 68th Algebra Symposium, Nagoya University, Japan MSJ
2023	Mar.	(1 week)	Arithmetic & Homotopic Galois Theory 2023, RIMS, Kyoto Univeristy, Japan AHGT IRN
2023	Feb.	(2 days)	Yufuin Workshop on Algebraic Geometry, Nippon Bunri University, Japan Google
2022	Nov.	(1 week)	Rationality, Moduli Spaces, and Related Topics, Nagoya University, Japan WordPress
2021	Mar.	(1 week)	Homotopic and Geometric Galois Theory, Zoom (Oberwolfach, Germany) MFO
2021	Feb.	(1 day)	Special lectures. In honor of Professor Shigefumi Mori's 70th Birthday, Zoom (Kyoto, Japan)
2021	Feb.	(3 days)	Degenerations and models of algebraic varieties and related topics, Zoom (Kobe, Japan) Google
2019	Nov.	(1 week)	The 41st Symposium on Commutative Algebra, Kurashiki Seaside Hotel, Japan Google
2019	Oct.	(1 week)	Kinosaki algebraic geometry symposium 2019, Kinosaki International Arts Center, Japan
2019	Sep.	(2 weeks)	National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan NTU
2019	Sep.	(1 week)	The 27th Summer School on Number Theory, Tohoku University of Community Service and Science, Koeki Hall, Japan Google
2019	Aug.	(3 weeks)	National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan NTU
2018	Mar.	(1 week)	Algebraic Geometry and Moduli Theory, Conference in Honor of Shigeru Mukai's Retirement, RIMS, Kyoto Univeristy, Japan Nagoya
2018	Jun.	(1 week)	Université Pierre-et-Marie-Curie (Paris VI) et Université Paris-Sud, Paris, Orsay, France
2018	Jun.	(1 day)	Séminaire N. Bourbaki, Institut Henri Poincaré, Paris, France ENS
2018	Jun.	(2 days)	International Workshop on Algebra, National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan NTU
2018	May	(3 days)	Profinite monodromy, Galois representations, and Complex functions, In honor of Professor Yasutaka Ihara's 80th Birthday, RIMS, Kyoto University, Japan RIMS
2018	Mar.	(1 week)	Motives in Tokyo, on the occasion of Shuji Saito's 60th Birthday, The University of Tokyo, Japan Chiba
2017	Dec.	(1 week)	Algebraic Number Theory and Related Topics 2017, RIMS, Kyoto University, Japan RIMS
2017	Oct.	(1 week)	Kinosaki algebraic geometry symposium 2017, Kinosaki International Arts Center, Japan Google
2017	Sep.	(1 week)	Workshop on p-adic L-functions and algebraic cycles, National Taiwan University, Taiwan NTU
2017	Aug.	(6 weeks)	National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan NTU
2017	Jul.	(1 week)	Iwasawa 2017, The University of Tokyo, Japan Tokyo
2017	Jun.	(3 days)	Journées Algophantiennes Bordelaises 2017, Institut de Mathématiques de Bordeaux, Université Bordeaux, France Bordeaux
2016	Nov.	(1 week)	Algebraic Number Theory and Related Topics 2016, RIMS, Kyoto University, Japan RIMS
2016	Oct.	(3 days)	Researches on isometries from various viewpoints, RIMS, Kyoto University, Japan
2016	Sep.	(1 week)	Japan-Taiwan Joint Conference on Number Theory 2016, National Taiwan University, Taiwan NTU
2016	Aug.	(7 weeks)	National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan NTU
2016	Jul.	(1 week)	Rationality and self-maps of algebraic varieties, RIMS, Kyoto University, Japan RIMS
2015	Sep.	(3 days)	New developments and progress in mathematics via computer algebra system, RIMS, Kyoto University, Japan Kanazawa
2015	Sep.	(3 days)	The 4th International Congress on Natural Sciences (ICNS2015), National Changhua University of Education, Taiwan NCUE
2015	Aug.	(4 weeks)	National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan NTU
2015	Jul.	(2 days)	Kálmán Győry 75 Symposium, University of Debrecen, Hungary Győry 75
2015	Jul.	(1 week)	29th Journées Arithmétiques (JA2015), University of Debrecen, Hungary JA2015
2015	Mar.	(1 week)	Joint Seminar and Reseach Camp (JSRC2015) CNiigata University, Japan JSRC2015
2014	Dec.	(1 week)	National Center for Theoretical Sciences (NCTS) Taipei Office, National Taiwan University, Taiwan NTU
2014	Sep.	(1 week)	New Developments in Algebraic Geometry, National Taiwan University, Taiwan NTU
2014	Aug.	(4 weeks)	National Center for Theoretical Sciences (NCTS) Taipei Office, National Taiwan University, Taiwan NTU
2014	Aug.	(2 weeks)	SEOUL ICM 2014, Coex, Seoul, Korea SEOUL ICM 2014
2014	Jul.	(1 week)	Kyoto Workshop on Algebraic Varieties and Automorphism Groups, RIMS, Kyoto University, Japan Niigata
2013	Oct.	(3 days)	The 3rd International Congress on Natural Sciences with Sisterhood Universities (ICNS2013), Niigata University, Japan ICNS2013
2013	Sep.	(1 day)	Nishi-Waseda Seminar on Number Theory, In honor of Professor Shizuo Endo's 80th Birthday, Waseda University, Japan
2013	Sep.	(1 week)	Thue 150, Institut de Mathématiques de Bordeaux, Université Bordeaux 1, France Thue 150
2013	Aug.	(3 weeks)	National Center for Theoretical Sciences (NCTS) Taipei Office, National Taiwan University, Taiwan NTU
2012	Dec.	(1 week)	Algebraic Number Theory and Related Topics, RIMS, Kyoto University, Japan Tokyo
2012	Aug.	(3 weeks)	National Center for Theoretical Sciences (NCTS) Taipei Office, National Taiwan University, TaiwanNTU
2011	Aug.	(5 weeks)	National Center for Theoretical Sciences (NCTS) Taipei Office, National Taiwan University, Taiwan NTU
2010	Oct.	(3 weeks)	Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taiwan TIMS
2009	Dec.	(1 week)	The Joint Conference of ASCM2009 and MACIS2009, JAL Resort Sea Hawk Hotel Fukuoka, Japan Kyushu
2008	Nov.	(1 week)	The Japan-Korea Joint Seminar on Number Theory and Related Topics 2008, Tohoku University, Japan Tohoku
2008	Aug.	(1 week)	The 5th Japan-China Seminar on Number Theory, Kinki University, Japan World Scientific
2008	Jun.	(1 week)	Foundations of Computational Mathematics, City University of Hong Kong, China FoCM'08
2007	Dec.	(1 week)	Algebraic Number Theory and Related Topics, RIMS, Kyoto University, Japan Osaka
2007	Jul.	(2 weeks)	National Center for Theoretical Sciences (NCTS) Taipei Office, National Taiwan University, Taiwan NTU
2007	Jun.	(1 week)	National Center for Theoretical Sciences (NCTS), Math. Division, National Tsing Hua University, Taiwan NCTS
2006	Dec.	(1 week)	International Conference on Number Theory, Harish-Chandra Research Institute (HRI), India HRI
2005	Sep	(1 week)	Galois groups and algebraic equations, Kagoshima University, Japan UEC
2005	Jul.	(1 day)	Vortrag in der Arbeitsgemeinschaft über Algebra, Technische Universität München, Germany
2005	May	(1 day)	Oberseminar Algebra-Zahlentheorie, Ruprecht-Karls-Universität Heidelberg, Germany
2005	May	(1 day)	Kolloquium in Universität des Saarlandes, Universität des Saarlandes Germany, Saarlandes
2004	Sep.	(1 year)	Guest Researcher of Prof. Manfred Knebusch, Universität Regensburg, Germany Regensburg

Research Interests

Preprints arXiv / Front for the arXiv

Papers MathSciNet / zbMATH / Algorithm [ Niigata | Kyoto | KURENAI 1 2 3 4 5 6 ]

Ph.D. Dissertation

Refereed Articles & Surveys

Honors

Research Grants

Research Grants (Co-Investigator)

Visits & Attendances