Research

My research interest is in commutative algebra. I am particularly interested in the theory of integral closure, multiplicity, and Rees algebra of ideals/modules. I am also interested in computational aspects of commutative algebra and its applications to mathematical and data sciences.

Papers:

• F. Hayasaka and V. Kodiyalam, Note on length and multiplicity of modules over two-dimensional regular local rings, accepted in Proceedings of the American Mathematical Society
• F. Hayasaka and H. Imamura, An example to a question of Ratliff on asymptotic prime divisors, accepted in Rocky Mountain Journal of Mathematics
• F. Hayasaka and V. Kodiyalam, Indecomposable integrally closed modules of rank 3 over two-dimensional regular local rings, Journal of Pure and Applied Algebra 228 (2024) Paper No. 107612, 18 pp.
• F. Hayasaka and V. Kodiyalam, Note on indecomposable integrally closed modules of rank 2 over two-dimensional regular local rings, Journal of Commutative Algebra 15 (2023) 513-518
• F. Hayasaka, Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring, Journal of Pure and Applied Algebra 226 (2022) Paper No. 107026, 26 pp.
• F. Hayasaka, Constructing indecomposable integrally closed modules over a two-dimensional regular local ring, Journal of Algebra 556 (2020), 879-907
• F. Hayasaka, A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules II, Communications in Algebra 47 (2019), 3250-3263
• F. Hayasaka, Asymptotic vanishing of homogeneous components of multigraded modules and its applications, Journal of Algebra 513 (2018), 1-26
• F. Hayasaka, A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules, Journal of Pure and Applied Algebra 222 (2018), 3774-3783
• F. Hayasaka, A computation of Buchsbaum-Rim functions of two variables in a special case, Rocky Mountain Journal of Mathematics 46 (2016), 1547-1557
• F. Hayasaka, Asymptotic periodicity of primes associated to multigraded modules, Communications in Algebra 42 (2014), 2769-2778
• F. Hayasaka, Asymptotic periodicity of grade associated to multigraded modules, Proceedings of the American Mathematical Society 140 (2012), 2279-2284
• F. Hayasaka and E. Hyry, On the Buchsbaum-Rim function of a parameter module, Journal of Algebra 327 (2011), 307-315
• F. Hayasaka and E. Hyry, A note on the Buchsbaum-Rim multiplicity of a parameter module, Proceedings of the American Mathematical Society 138 (2010), 545-551
• S. Goto, F. Hayasaka and R. Takahashi, On vanishing of certain Ext modules, Journal of the Mathematical Society of Japan 60 (2008), 1045-1064
• F. Hayasaka and E. Hyry, A family of graded modules associated to a module, Communications in Algebra 36 (2008), 4201-4217
• F. Hayasaka, Asymptotic stability of primes associated to homogeneous components of multigraded modules, Journal of Algebra 306 (2006), 535-543
• S. Goto, F. Hayasaka, K. Kurano and Y. Nakamura, Rees algebras of the second syzygy module of the residue field of a regular local ring, Contemporary Mathematics 390 (2005), 97-108
• S. Goto, F. Hayasaka and S. Kasuga, Towards a theory of Gorenstein m-primary integrally closed ideals, NATO Science Series II: Mathematics, Physics and Chemistry 115 (2003), 159-177
• S. Goto, F. Hayasaka and S. Iai, The a-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings, Proceedings of the American Mathematical Society 131 (2003), 87-94
• S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals II, Journal of Mathematics Kyoto University 42 (2002), 631-639
• S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals, Proceedings of the American Mathematical Society 130 (2002), 3159-3164

Preprint:

• F. Hayasaka, Modules of reduction number one, arXiv:math/0612741 [math.AC]

Talks:

• 早坂太, 加群の重複度と長さに関する一注意, 霧島ミニシンポジウム, 2025年10月31日（国分パークプラザ）
• 早坂太, 2次元正則局所環上の位数2の整閉イデアルに付随する整閉加群について, 東京可換環論セミナー, 2025年3月28日（オンライン）
• Futoshi Hayasaka, Topics in integral closure of modules, Interactions of Commutative Algebra, Representation theory and Combinatorics in Bangkok, 2024年10月31日（The Meiji University ASEAN Center）
• 早坂太, 2次元正則局所環上の階数2の整閉加群の分類について, 明治大学可換環論セミナー, 2024年7月27日（明治大学駿河台キャンパス）
• 早坂太, 位数2の整閉イデアルに付随する階数2の整閉加群, 第35回可換環論セミナー, 2024年6月11日（徳島大学）
• 早坂太, 2次元正則局所環上の整閉加群の分類に向けて, 第2回札幌可換環論セミナー, 2024年3月7日（北海道教育大学札幌駅前サテライト）
• 早坂太, On a question of Ratliff on the associated primes of powers of an ideal, OCAMI 可換環論・不変式論セミナー III, 2024年1月12日（大阪公立大学杉本キャンパス）
• 早坂太・今村青斗, An example to a question of Ratliff on asymptotic prime divisors, 第44回可換環論シンポジウム, 2023年11月25日（レクトーレ葉山）
• 早坂太, 直既約整閉加群に付随する行列式イデアルについて, 岡山可換代数表現セミナー（OSCAR）, 2023年4月24日（岡山大学環境理工棟）
• Futoshi Hayasaka, Ideals of indecomposable integrally closed modules over two-dimensional regular local rings, The 11th Japan-Vietnam Joint seminar on Commutative Algebra, by and for young mathematicians, 2023年3月30日（Institute of Mathematics, VAST）
• 早坂太, On ideals of indecomposable integrally closed modules over two-dimensional regular local rings, 第43回可換環論シンポジウム, 2022年11月18日（大阪大学南部陽一郎ホール）
• 早坂太, ２次元正則局所環上の直既約整閉加群について, 特異点セミナー, 2022年7月25日（日本大学文理学部）
• 早坂太, ２次元正則局所環上の階数２の直既約整閉加群, 第33回可換環論セミナー, 2022年6月16日（オンライン）

Lectures:

• 早坂太, 多項式の割り算 -1変数から多変数へ-, 令和7年度岡山県高教研数学部会美作支部研究会, 2025年5月19日（岡山県立林野高等学校）
• 早坂太, 名古屋大学大学院多元数理科学研究科集中講義「代数学特別講義III」（2次元正則局所環上の整閉加群）, 2024年7月1日〜7月5日（名古屋大学）