معرفی
Ryo Fujita serves as an Assistant Professor at the Research Institute for Mathematical Sciences (RIMS), Kyoto University, a position he has held since April 2021. His research focuses on the representation theory of algebras arising from simple Lie algebras or their root systems, including quantum groups and Hecke algebras. Fujita's work particularly examines the structure of module categories and related geometric objects, with significant contributions to the theory of affine quantum groups, quiver varieties, R-matrices, and quantum Grothendieck rings.
His educational journey at Kyoto University spans from undergraduate studies (2010-2014) to doctoral degree (awarded in March 2019). The key milestones include:
- Bachelor of Science, Faculty of Science, Kyoto University (2010-2014)
- Master of Science, Graduate School of Science, Division of Mathematics, Kyoto University (2014-2016)
- Doctor of Science, Graduate School of Science, Division of Mathematics, Kyoto University (2016-2019)
Fujita's research interests lie at the intersection of algebra, geometry, and representation theory. He specializes in quantum groups, R-matrices, quiver varieties, and cluster algebras, with a focus on affine quantum groups. His investigations into the module categories of these algebras have uncovered deep connections to geometric representation theory and categorification. Fujita's work often bridges abstract algebraic structures with combinatorial and geometric frameworks, advancing the understanding of quantum symmetries and their applications.
Analysis of Fujita's publications from 2018 to 2024 reveals a cohesive research trajectory centered on quantum affine algebras and related structures. His work consistently explores deformed Cartan matrices, generalized preprojective algebras, quantum Grothendieck rings, and the singularities of R-matrices. A notable trend is the interplay between algebraic representation theory and geometric constructions like quiver varieties, often mediated by cluster algebra structures. This approach has led to significant advances in understanding the categorical and combinatorial aspects of quantum group representations.
Fujita currently leads a Grant-in-Aid for Early-Career Scientists (2023-2026) titled "Study on the representations of affine quantum groups using quivers with potentials". He is also a key participant in a major Grant-in-Aid for Scientific Research (S) project (2021-2026) on "Representation theory of vertex algebras for the 21st century". Previously, he held a JSPS Research Fellowship (2018-2020) supporting his foundational work on quantum affine algebras.
Based at RIMS, Kyoto University, Fujita is embedded in one of Japan's premier mathematical research environments. He collaborates closely with mathematicians including Kota Murakami and Hironori Oya, as evidenced by joint publications. His research group and collaborations extend internationally, with presentations at institutions worldwide, reflecting the global impact of his work in representation theory.
