The main research theme of our group is developing and explicating fundamental theories for mathematical models via applications of commutative algebra and probability theory to computational algebra and stochastic models.
My research interests lie in commutative algebra, homological algebra, and combinatrics. Among these topics, I am particularly interested in the theory of integral closure and multiplicity for modules. I am also interested in computational aspects of commutative algebra and its applications to mathematical and data sciences.
My research field is probability theory and related topics. I mainly conduct research on random matrices, which are important probability models. This includes developing a general theory, performing specific calculations, and exploring potential applications. In particular, I am interested in particle systems motivated by random matrices, and my main focus is the analysis on stochastic processes corresponding to infinite particle systems.