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Name | Akinari Hoshi |

Sex | Male |

Place of birth | Yokohama, Japan |

Nationality | Japanese |

Mar. 15, 2003 M.Sc., Waseda University

Mar. 15, 2005 Ph.D. (D.Sc.), Waseda University

Apr. 2004 - Mar. 2005 | Research Fellow of the Japan Society for the Promotion of Science (DC2) |

Apr. 2005 - Mar. 2006 | Research Fellow of the Japan Society for the Promotion of Science (PD) |

Apr. 2006 - Mar. 2008 | Research Associate, Department of Mathematics, School of Education, Waseda University |

Apr. 2008 - Mar. 2013 | Assistant Professor, Department of Mathematics, Faculty of Science, Rikkyo University |

Apr. 2013 - present | Associate Professor, Department of Mathematics, Faculty of Science, Niigata University |

2016 | Niigata University President's Award |

2004 - 2005 | Grant-in-Aid for JSPS Fellows 04J01682 1,900,000 yen |

2006 | Waseda University Grant for Special Research Projects (2006A-850) 200,000 yen |

2007 | Waseda University Grant for Special Research Projects (2007B-067) 450,000 yen |

2008 | Rikkyo University Special Fund for Research 500,000 yen |

2009 | Rikkyo University Special Fund for Research 500,000 yen |

2010 - 2012 | Grant-in-Aid for Young Scientists (B) 22740028 2,340,000 yen |

2013 - 2016 | Grant-in-Aid for Scientific Research (C) 25400027 4,810,000 yen |

2016 | Niigata University President's Award (Research Grant for Young Researchers) 800,000 yen |

2017 | Niigata University Grant-in-Aid for Scientific Research Application Support Program 700,000 yen |

2018 | Niigata University Grant-in-Aid for International Conference Participation Support Project 200,000 yen |

2019 - 2022 | Grant-in-Aid for Scientific Research (C) 19K03418 4,290,000 yen |

- A. Hoshi, Multiplicative quadratic forms on algebraic varieties,

Proc. Japan Acad. Ser. A 79 (2003) 71-75. - A. Hoshi, Noether's problem for some meta-abelian groups of small degree,

Proc. Japan Acad. Ser. A 81 (2005) 1-6. - K. Hashimoto, A. Hoshi,
Families of cyclic polynomials obtained from geometric generalization
of Gaussian period relations,

Math. Comp. 74 (2005) 1519-1530. - K. Hashimoto, A. Hoshi,
Geometric generalization of Gaussian period relations with application to
Noether's problem for meta-cyclic groups,

Tokyo J. Math. 28 (2005) 13-32. - A. Hoshi, Explicit lifts of quintic Jacobi sums and period polynomials for
F
_{q},

Proc. Japan Acad. Ser. A 82 (2006) 87-92. - A. Hoshi, K. Miyake,
Tschirnhausen transformation of a cubic generic polynomial and a 2-dimensional
involutive Cremona transformation,

Proc. Japan Acad. Ser. A 83 (2007) 21-26. - K. Hashimoto, A. Hoshi, Y. Rikuna,
Noether's problem and Q-generic polynomials for the normalizer of the
8-cycle in S
_{8}and its subgroups,

Math. Comp. 77 (2008) 1153-1183. - A. Hoshi, Y. Rikuna,
Rationality problem of three-dimensional purely monomial group actions: the last case,

Math. Comp. 77 (2008) 1823-1829. - A. Hoshi, M. Kang,
A rationality problem of some Cremona transformation,

Proc. Japan Acad. Ser. A 84 (2008) 133-137. - A. Hoshi, K. Miyake,
A geometric framework for the subfield problem of generic polynomials via Tschirnhausen
transformation,

Number theory and applications, 65-104, Hindustan Book Agency, New Delhi, 2009. - A. Hoshi, K. Miyake,
On the field intersection problem of quartic generic
polynomials via formal Tschirnhausen transformation,

Comment. Math. Univ. St. Pauli 58 (2009) 51-86. - A. Hoshi,
On the simplest quartic fields and related Thue equations,

The Joint Conference of ASCM 2009 and MACIS 2009, 320-329, COE Lect. Note 22, Kyushu Univ. Fac. Math., Fukuoka, 2009.

Computer Mathematics, Springer, 67-85, 2014. - A. Hoshi, K. Miyake,
A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations,

Interdiscip. Inform. Sci. 16 (2010) 45-54, Special Section: Japan-Korea Joint Seminar on Number Theory and Related Topics 2008. - A. Hoshi, K. Miyake,
On the field intersection problem of solvable quintic generic polynomials,

Int. J. Number Theory 6 (2010) 1047-1081. - A. Hoshi, M. Kang,
Twisted symmetric group actions,

Pacific J. Math. 248 (2010) 285-304. - A. Hoshi, H. Kitayama, A. Yamasaki,
Rationality problem of three-dimensional monomial group actions,

J. Algebra 341 (2011) 45-108. - A. Hoshi,
On correspondence between solutions of a family of cubic Thue equations and
isomorphism classes of the simplest cubic fields,

J. Number Theory 131 (2011) 2135-2150. - A. Hoshi,
On the simplest sextic fields and related Thue equations,

Funct. Approx. Comment. Math. 47 (2012) 35-49. - A. Hoshi, M. Kang, B. E. Kunyavskii,
Noether's problem and unramified Brauer groups,

Asian J. Math. 17 (2013) 689-714. - A. Hoshi, M. Kang, H. Kitayama,
Quasi-monomial actions and some 4-dimensional rationality problems,

J. Algebra 403 (2014) 363-400. - A. Hoshi,
On Noether's problem for cyclic groups of prime order,

Proc. Japan Acad. Ser. A 91 (2015) 39-44. - H. Chu, A. Hoshi, S.-J. Hu, M. Kang,
Noether's problem for groups of order 243,

J. Algebra 442 (2015) 233-259. - A. Hoshi,
Birational classification of fields of invariants for groups of order 128,

J. Algebra 445 (2016) 394-432. - A. Hoshi, M. Kang, A. Yamasaki,
Degree three unramified cohomology groups,

J. Algebra 458 (2016) 120-133. - Complete solutions to a family of Thue equations of degree 12,

J. Théor. Nombres de Bordeaux 29 (2017) 549-568. - A. Hoshi, A. Yamasaki,
Rationality problem for algebraic tori,

Mem. Amer. Math. Soc. 248 (2017) no. 1176, v+215 pp. - A. Hoshi, M. Kang, A. Yamasaki,
Rationality problems for relation modules of dihedral groups,

J. Algebra 530 (2019) 368-401. - A. Hoshi, H. Kitayama,
Three-dimensional purely quasi-monomial actions,

to appear in Kyoto J. Math. - S. Hasegawa, A. Hoshi, A. Yamasaki,
Rationality problem for norm one tori in small dimensions,

to appear in Math. Comp. - A. Hoshi, M. Kang, A. Yamasaki,
Degree three unramified cohomology groups and Noether's problem for groups of order 243,

to appear in Journal of Algebra.

- A. Hoshi, K. 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). - A. Hoshi, K. 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., 2010. - A. Hoshi,
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).

Waseda University, March 2005.

Sep. 2004 - Mar. 2005 | Guest Researcher of Prof. Manfred Knebusch, Regensburg University, Germany |

as a JSPS Fellow (DC2) | |

Apr. 2005 - Jul. 2005 | Guest Researcher of Prof. Manfred Knebusch, Regensburg University, Germany |

as a JSPS Fellow (PD) |

- Noether's problem and Q-generic polynomials, Kolloquium in Universität des Saarlandes (invited by Prof. Rainer Schulze-Pillot), Universität des Saarlandes, Germany, May 27, 2005
- Noether Problems and Q-Generic Polynomials
for the Normalizer of the 8-Cycle in S
_{8}, Oberseminar Algebra-Zahlentheorie (invited by Prof. B. Heinrich Matzat), Ruprecht-Karls-Universität Heidelberg, Germany , May 30, 2005 - Noether's problem and Q-generic polynomials
for the normalizer of the 8-cycle in S
_{8}and its subgroups, Vortrag in der Arbeitsgemeinschaft über Algebra (invited by Prof. Gregor Kemper), Technische Universität München, Germany, July 5, 2005 - Noether's problem for Frobenius groups of prime degree up to 23, Conference: Galois groups and algebraic equations (invited by Prof. Ki-ichiro Hashimoto, Masanari Kida and Nobuhiro Terai), Kagoshima Univ., Sep. 5, 2005
- (with Katsuya Miyake) Tschirnhausen Transformation of a Cubic Generic Polynomial and a 2-dimensional Involutive Cremona Transformation, International Conference on Number Theory (invited by Prof. Balakrishnan Ramakrishnan and Kalyan Chakraborty), Harish-Chandra Research Institute, India, Dec. 1, 2006
- Tschirnhausen transformation of a cubic generic polynomial and a 2-dimensional involutive Cremona transformation, as a part of NCTS Short Course on Number Theory given by K. Miyake (invited by Prof. Wen-Ching Winnie Li and Jing Yu) National Center for Theoretical Sciences, Math. Division in National Tsing Hua University, Taiwan, June 27, 2007
- Cubic generic polynomials and some Cremona transformations (joint work with K. Miyake), Seminar of Algebra (invited by Prof. Ming-chang Kang), National Center for Theoretical Sciences, Math. Division (Taipei Office) in National Taiwan University, Taiwan, July 26, 2007
- On the field intersection problem of generic polynomials via resolvent polynomials, Foundations of Computational Mathematics (FoCM'08) WORKSHOP C4 Computational number theory (invited by Prof. Hendrik Lenstra, Takakazu Satoh and Peter Stevenhagen), City University of Hong Kong, China, June 24, 2008
- (with Katsuya Miyake) Some Diophantine problems arising from the isomorphism problem of generic polynomials, The 5th Japan-China Seminar on Number Theory (invited by Prof. Shigeru Kanemitsu), Kinki Univ., Japan, Aug. 27, 2008
- (with Katsuya Miyake) On the field isomorphism problem of generic polynomials via formal Tschirnhausen transformation, The Japan-Korea Joint Seminar on Number Theory and Related Topics 2008 (invited by Prof. Hisao Taya), Tohoku Univ., Japan, Nov. 12, 2008
- On correspondence between solutions of a parametric family of cubic Thue equations and isomorphism classes of simplest cubic fields, Diophantine Analysis and Related Fields 2009 (DARF 2009) (invited by Prof. Noriko Hirata-Kohno, Masaaki Amou, Ryotaro Okazaki, Takao Komatsu and Isao Wakabayashi), Nihon Univ., Mar. 2, 2009
- On the simplest quartic fields and related Thue equations, The Joint Conference of ASCM2009 and MACIS2009, ASCM2009 Special Session on Computational Algebraic Number Theory (invited by Prof. Guenael Renault and Kazuhiro Yokoyama), JAL Resort Sea Hawk Hotel Fukuoka, Japan, Dec. 16, 2009
- Rationality problem of three-dimensional monomial group actions (joint work with H. Kitayama and A. Yamasaki), The 5th Affine Algebraic Geometry Meeting (invited by Prof. Kayo Masuda, Hideo Kojima and Takashi Kishimoto), Kwansei Gakuin Univ., Mar. 5, 2010
- Three-dimensional monomial group actions (joint work with H. Kitayama and A. Yamasaki), TIMS Lecture, Taida Institute for Mathematical Sciences (invited by Prof. Ming-chang Kang), National Taiwan University, Taiwan, Oct. 22, 29, 2010
- On the simplest sextic fields and related Thue equations, One-day workshop of algebra (invited by Prof. Ming-chang Kang), NCTS/TPE, National Taiwan Univ., Taiwan, Aug. 16, 2011.
- Quasi-monomial actions and some 4-dimensional rationality problems, The 9th Affine Algebraic Geometry Meeting (invited by Prof. Takashi Kishimoto, Hideo Kojima and Shigeru Kuroda), Kwansei Gakuin Univ., Mar. 3, 2012
- Rationality problem of algebraic tori (I) (joint work with A. Yamasaki), One-day workshop of algebra (invited by Prof. Ming-chang Kang), NCTS/TPE, National Taiwan Univ., Taiwan, Aug. 16, 2012.
- Rationality problem for fields of invariants: a survey, One-day workshop of algebra (invited by Prof. Ming-chang Kang), NCTS/TPE, National Taiwan Univ., Taiwan, Aug. 19, 2013.
- (with Aiichi Yamasaki) Rationality problem for algebraic tori, SEOUL ICM 2014, Short Communications, Coex, Seoul, Korea, Aug. 19, 2014.
- Birational classification of fields of invariants for groups of order 128, New Developments in Algebraic Geometry (invited by Prof. Caucher Birkar, Jungkai Alfred Chen, Wu-Yen Chuang and Jeng-Daw Yu), NCTS/TPE, National Taiwan Univ., Taiwan, Sep. 5, 2014.
- On the simplest number fields and related Thue equations, 29th Journées Arithmétiques (JA2015), University of Debrecen, Hungary, Jul. 9, 2015.
- On the simplest number fields and related Thue equations, The 4th International Congress on Natural Sciences (ICNS2015), Changhua, Taiwan, Sep. 10, 2015.
- Rationality problem for fields of invariants, Workshop: Rationality and selfmaps of algebraic varieties (invited by Prof. Shigeru Mukai and Keiji Oguiso), RIMS, Kyoto Univ., Japan, Jul. 21, 2016.
- Rationality problem for fields of invariants, Japan-Taiwan Joint conference on Number theory 2016 (invited by Prof. Ming-Lun Hsieh and Masataka Chida), NCTS/TPE, National Taiwan Univ., Taiwan, Sep. 9, 2016.
- Rationality problem for fields of invariants, Workshop: Researches on isometries from various viewpoints (invited by Prof. Takeshi Miura), RIMS, Kyoto Univ., Jpan, Oct. 31, 2016.
- Rationality problem for fields of invariants, The 15th Affine Algebraic Geometry Meeting (invited by Prof. Hideo Kojima, Takashi Kishimoto, Adrien Dubouloz and Kayo Masuda), Kwansei Gakuin Univ., Mar. 5, 2017.
- Cubic Thue equations and simplest cubic fields, Journées Algophantiennes Bordelaises 2017 (invited by Prof. Yuri Bilu), Institut de Mathématiques de Bordeaux, Université Bordeaux, France, Jun. 8, 2017.
- Unramified Brauer group of multiplicative invariant fields of dimension ≤ 6 (I), NCTS Seminar on Algebra (invited by Prof. Ming-chang Kang), NCTS, National Taiwan Univ., Taiwan, Sep. 20, 2017.
- Rationality problem for fields of invariants, Kinosaki algebraic geometry symposium 2017 (invited by Prof. Taro Fujisawa, Takuzo Okada and Taro Sano), Kinosaki International Arts Center, Oct. 25, 2017.
- Rationality problem for fields of invariants and unramified cohomology groups, International Workshop on Algebra (invited by Prof. Jungkai Alfred Chen and Chia-Fu Yu), NCTS, National Taiwan Univ., Taiwan, Jun. 9, 2018.
- Degree three unramified cohomology groups and Noether's problem for groups of order 243, Séminaire "Variétés Rationnelles" (invited by Prof. Jean-Louis Colliot-Thélène, Cyril Demarche and Mathieu Florence), Université Pierre-et-Marie-Curie (Paris VI), France, Jun. 22, 2018.
- Degree three unramified cohomology groups and Noether's problem for groups of order 243, NCTS Seminar on Algebra (invited by Prof. Ming-chang Kang), NCTS, National Taiwan Univ., Taiwan, Aug. 12, 2019.