Applied Mathematics
Staff
Research Topics
The main research theme of our group is developing and explicating fundamental theories for mathematical models in environmental life science via applications of commutative algebra and probability theory to computational algebra and stochastic models.
Commutative Algebra
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My research interests lie in commutative algebra, homologival algebra, and combinatrics. Among these topics, I am particularly interested in the theory of Buchsbaum-Rim multiplicity and integral closure for modules, and the ring structure of Rees algebra of modules. |
Stochastic Process Theory
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The main research theme is multidimensional discrete distributions using analytic number theory, and their applications to stochastic processes. We study new mathematical structures that include multidimensional stochastic models in environmental life science through multivariable multiple zeta functions and Euler products. |
Publication List
- F. Hayasaka, Constructing indecomposable integrally closed modules over a two-dimensional regular local ring. J. Algebra 556, 879-907 (2020)
- F. Hayasaka, A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules II, Communications in Algebra 47, Issue 8, 3250-3263 (2019)
- F. Hayasaka, Asymptotic vanishing of homogeneous components of multigraded modules and its applications, J. Algebra 513, 1-26 (2018)
- F. Hayasaka, A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules, Journal of Pure and Applied Algebra 222, 3774-3783 (2018)
- F. Hayasaka, A computation of Buchsbaum-Rim functions of two variables in a special case, Rocky Mountain Journal of Mathematics, Volume 46, Number 6, 1547-1557 (2016)