Doctor of Philosophy (Mathematical Science)

No

Ring theory, Representation theory

My research subject is representation theory of algebras. Given a ring (like a quiver or a commutative ring), its representation theory is about the study of categories (primarily the module category) and various related structures. I am particularly interested in homological structures appearing in Cohen-Macaulay representation theory of finite dimensional algebras or of commutative Gorenstein rings. I am mainly studying tilting theory linking their representation theories and also the theory of cluster tilting objects (or non-commutative resolutions) for these rings, through triangulated categories like derived categories, singularity categories, and cluster categories, and their enhancements by differential graded categories.

Research Interests

• Calabi-Yau structures on differential graded categories
  keyword : dg category, Calabi-Yau structure, singularity category, cluster category
  2022.04～2025.03.

Academic Activities Membership in Academic Society

• The Mathematical Society of Japan