Basic Information

Affiliated programs (koza)

• Graduate School of Science, 数学・数理解析専攻 応用数理講座, 助教

Professional Memberships

• From Apr. 2018, To Present

  The Mathematical Society of Japan

Academic Degree

• 博士（理学）(京都大学)
• 修士（理学）(京都大学)

Research History

• From Apr. 2021, To Present

  Kyoto University, Research Institute for Mathematical Sciences, Assistant professor
• From Oct. 2020, To Sep. 2022

  Université de Paris, IMJ-PRG, Post-doctoral researcher (JSPS overseas research fellow)
• From Aug. 2020, To Oct. 2020

  The University of Tokyo, Kavli IPMU, Project Researcher
• From Apr. 2020, To Aug. 2020

  Kyoto University, Graduate School of Science Division of Mathematics, Research Associate
• From Apr. 2019, To Mar. 2020

  Kyoto University, Graduate School of Science Division of Mathematics, JSPS Research Fellow (PD)
• From Mar. 2018, To Mar. 2019

  Kyoto University, Graduate School of Science Division of Mathematics, JSPS Research Fellow (DC2)

Profile

• Profile

  I am working on representation theory of algebras related to complex semisimple Lie algebras or their root systems, with a particular focus on affine quantum groups.

ID,URL

• ORCID ID

  0000-0003-4905-2402

• J-Global ID

  202001010407465468

• Researcher number

  40972477

• External link

  https://rfujitam.github.io/index.html

researchmap URL

• https://researchmap.jp/ryo_fujita

Research

Research Topics, Overview of the research

• Research Topics

  Representation Theory

• Overview of the research

  I am working on the representation theory of algebras related to complex semisimple Lie algebras and their root systems (such as Hecke algebras, quantum groups etc.) with particular interests in their module categories and related geometric structures. Currently, my research tends to focus on the representation theory of quantum affine algebras.

Research Interests

• R-matrix
• quiver variety
• cluster algebra
• Quantum Group
• Representation Theory

Research Areas

• Natural sciences, Algebra

Papers

• Singularities of normalized R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Annals of Representation Theory, 17 Jun. 2026, Peer-reviewed

  
• Monoidal Jantzen filtrations

  Ryo Fujita; David Hernandez

  Advances in Mathematics, Jun. 2026, Peer-reviewed

  
• Inflations among quantum Grothendieck rings of type A

  Ryo Fujita

  Journal of Algebraic Combinatorics, Nov. 2025, Peer-reviewed

  Access this paper :

  
• Deformed Cartan matrices and generalized preprojective algebras II: general type

  Ryo Fujita; Kota Murakami

  Mathematische Zeitschrift, Dec. 2023, Peer-reviewed

  Access this paper :

  
• Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

  Ryo Fujita

  Selecta Mathematica, Feb. 2022, Peer-reviewed

  Access this paper :

  
• Q-data and Representation Theory of Untwisted Quantum Affine Algebras

  Ryo Fujita; Se-jin Oh

  Communications in Mathematical Physics, Jun. 2021, Peer-reviewed

  
• Coherent IC-sheaves on type $A_{n}$ affine Grassmannians and dual canonical basis of affine type $A_{1}$

  Michael Finkelberg; Ryo Fujita

  Representation Theory of the American Mathematical Society, 28 Jan. 2021, Peer-reviewed

  
• Geometric Realization of Dynkin Quiver Type Quantum Affine Schur–Weyl Duality

  Ryo Fujita

  International Mathematics Research Notices, 09 Oct. 2018, Peer-reviewed

  
• Tilting modules of affine quasi-hereditary algebras

  Ryo Fujita

  Advances in Mathematics, Jan. 2018, Peer-reviewed

  
• Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types

  Ryo Fujita

  Representation Theory of the American Mathematical Society, 18 Mar. 2022, Peer-reviewed

  
• Isomorphisms among quantum Grothendieck rings and propagation of positivity

  Ryo Fujita; David Hernandez; Se-jin Oh; Hironori Oya

  Journal für die reine und angewandte Mathematik (Crelles Journal), 01 Apr. 2022, Peer-reviewed

  
• Deformed Cartan Matrices and Generalized Preprojective Algebras I: Finite Type

  Ryo Fujita; Kota Murakami

  International Mathematics Research Notices, 25 Mar. 2022, Peer-reviewed

  

Misc.

• Partial $F$-invariants and cluster categorifications

  Peigen Cao; Ryo Fujita; Kota Murakami

  Preprint arXiv:2609.08781, 08 Sep. 2026

  
• Freezing operators in representation theory of quantum loop algebras

  Ryo Fujita; Fan Qin

  Preprint arXiv:2601.00687, 02 Jan. 2026

  
• Isomorphisms among quantum Grothendieck rings and cluster algebras

  Ryo Fujita; David Hernandez; Se-jin Oh; Hironori Oya

  Preprint arXiv:2304.02562, 05 Apr. 2023

  

Presentations

• On the Hernandez conjecture

  Ryo Fujita

  Coulomb branches and affine quantum groups, 06 Jul. 2026, Invited

  
• On the Hernandez conjecture

  Ryo Fujita

  QAMGAST2026, 13 Jan. 2026, SIMIS, Invited

  
• On the pole order of normalized R-matrices for reachable modules

  Ryo Fujita

  Quantum groups, Monoidal Categorification and Related Topics, 17 Dec. 2025, QSMS Center for Quantum Structures in Modules and Spaces, Invited

  
• Applications of freezing operator to the representation theory of quantum loop algebras

  Ryo Fujita

  RIMS Symposium ``Confluence of combinatorics and representation theory'', 22 Oct. 2025

  
• Introduction to Representation Theory of Affine Quantum Groups

  Ryo Fujita

  46th RIMS Public Lectures (in Japanese)

  
• Singularities of R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Vertex Algebras & Integrable Systems, 07 Jul. 2025

  
• Singularities of R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Seminario de Álgebra Homológica (virtual), 02 Jul. 2025, Universidad de Buenos Aires, Invited

  
• Singularities of R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  RTISART-25 (Representation Theory, Integrable Systems, and Related Topics), 02 Jun. 2025, Invited

  
• Singularities of R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Seinar @ Beijing Normal University, 28 May 2025, Invited

  
• Singularities of R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Minami Osaka Daisuu Seminar, 28 Mar. 2025, Osaka Metropolitan University, Invited

  
• 

  Deformed Cartan matrices and generalized preprojective algebras, with application to quantum affine algebras

  Ryo Fujita

  Combinatorics And Representation Theory Seminar (online), 31 Oct. 2024, Invited

  
• Singularities of normalized R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Representation Theory Seminar, 17 Oct. 2024, Invited

  
• On a deformation of Grothendieck ring by using R-matrices

  Ryo Fujita

  Tokyo Tech Representation Theory Seminar, 26 Jul. 2024, Invited

  
• Isomorphisms among quantum Grothendieck rings and their cluster theoretical interpretation

  Ryo Fujita

  XXVII Brazilian Algebra Meeting, 16 Jul. 2024, Invited

  
• Symmetries and representation theory (for general audience)

  Ryo Fujita

  Soir\'ee Scientifique, 17 Jan. 2023, Invited

  
• Affine highest weight category and Schur-Weyl duality

  Ryo Fujita

  Representation Theory Seminar, 19 Oct. 2017, Invited

  
• Singularity of normalized R-matrices and E-invariants for Dynkin quivers

  Ryo Fujita

  Spring Workshop on the Representation Theory of Algebras and related topics, 22 Apr. 2024, Invited

  
• Isomorphisms among quantum Grothendieck rings and their cluster theoretical interpretation

  Ryo Fujita

  Mathematical Physics Seminar (online), 13 Feb. 2024, Invited

  
• Quantum affine algebras, graded quiver varieties, and generalized Schur-Weyl duality (3 talks)

  Ryo Fujita

  Physical Mathematics and Beyond --The first Workshop--, 29 Jan. 2024, Invited

  
• Quantum Grothendieck rings and their quantum cluster algebra structures

  Ryo Fujita

  Tokyo Nagoya Algebra Seminar (online), 11 Jan. 2024, Invited

  
• Quantum loop algebras and quantum Grothendieck rings

  Ryo Fujita

  Mathematics Seminar, 28 Nov. 2023, Invited

  
• Isomorphisms among quantum Grothendieck rings and their cluster theoretical interpretation

  Ryo Fujita

  Algebraic and Combinatorial Methods in Representation Theory, 23 Nov. 2023, Invited

  
• Isomorphisms among quantum Grothendieck rings and their cluster theoretical interpretation

  Ryo Fujita

  Cluster algebra, Representation theory and Algebraic geometry, 07 Sep. 2023, Invited

  
• On the quantum Grothendieck rings

  Ryo Fujita

  68th Algebra Symposium, 01 Sep. 2023, Invited

  
• Isomorphisms among quantum Grothendieck rings and their cluster theoretical interpretation

  Ryo Fujita

  Representation Theory Seminar, 17 Aug. 2023, Invited

  
• Quantum affine algebras and Quantum Grothendieck rings (6 hours online mini-course)

  Ryo Fujita

  ECNU Summer School on Lie theory, Invited

  
• Isomorphisms among quantum Grothendieck rings and their cluster theoretical interpretation

  Ryo Fujita

  Cluster algebras and related topics in East Asia, 19 Jun. 2023, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras

  Ryo Fujita

  Online seminar, 06 Jun. 2023, Invited

  
• Isomorphisms among quantum Grothendieck rings and their applications

  Ryo Fujita

  Integrable Systems and Quantum Groups —In Honor of Masato Okado's 60th Birthday—, 04 Mar. 2023, Invited

  
• Isomorphisms among quantum Grothendieck rings and their applications

  Ryo Fujita

  Workshop on interactions between representation theory, combinatorics, and geometry, 07 Jan. 2023, Invited

  
• Isomorphisms among quantum Grothendieck rings and their applications

  Ryo Fujita

  Algebra Days in Paris in honor of Bernhard Keller, 06 Sep. 2022, Invited

  
• Monoidal Jantzen filtrations for quantum affine algebras

  Ryo Fujita

  Geometric Representation Theory (Satellite Conference of vICM2022), 27 Jun. 2022, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras

  Ryo Fujita

  Hodge seminar (online), 10 Mar. 2022, Invited

  
• Monoidal Jantzen filtrations for quantum affine algebras

  Ryo Fujita

  QUANTUM GROUPS AND CLUSTER ALGEBRAS (online), 17 Feb. 2022, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras

  Kota Murakami; Ryo Fujita

  S\'eminaire d'alg\`ebre, 22 Nov. 2021, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras

  Ryo Fujita

  Lie Algebras and Applications (online seminar), 14 Dec. 2021, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras

  Ryo Fujita

  S\'eminaire d'alg\`ebre et de g\'eom\'etrie, 16 Nov. 2021, Invited

  
• Monoidal Jantzen filtrations for quantum affine algebras

  Ryo Fujita

  Oberwolfach workshop: Enveloping Algebras and Geometric Representation Theory, 04 Nov. 2021, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras

  Ryo Fujita

  S\'eminaire de Math\'ematique-Physique, 27 Oct. 2021, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras of finite type

  Ryo Fujita

  Oberwolfach mini-workshop: Three facets of R-matrices, 19 Oct. 2021, Invited

  
• Monoidal Jantzen filtrations for quantum affine algebras

  Ryo Fujita

  S\'eminaires : Groupes, Repr\'esentations et G\'eom\'etrie, 15 Oct. 2021, Invited

  
• Deformed Cartan matrices and generalized preprojective algebras of finite type

  Ryo Fujita

  Infinite Analysis 21: Around Cluster Algebras (online), 29 Sep. 2021, Invited

  
• On Schur--Weyl duality and its variants

  Ryo Fujita

  Paris Wakabutsu Meeting, 18 Sep. 2021, Invited

  
• Positivity of an analog of Kazhdan-Lusztig polynomials for finite-dimensional representations of quantum loop algebra

  Ryo Fujita

  Colloque Tournant 2021 du GDR Th\'eorie de Lie Alg\'ebrique et G\'eom\'etrique (online), 25 Mar. 2021, Invited

  
• Isomorphisms among quantum Grothendieck rings and propagation of positivity

  Ryo Fujita

  S\'eminaire d'alg\`ebre (online), 08 Mar. 2021, Invited

  
• Positivity of an analog of Kazhdan-Lusztig polynomials for finite-dimensional representations of quantum loop algebra

  Ryo Fujita

  16th Algebra-Analysis-Geometry Seminar (online), 17 Feb. 2021, Invited

  
• Positivity of an analog of Kazhdan-Lusztig polynomials for finite-dimensional representations of quantum affine algebra

  Ryo Fujita

  S\'eminaire d'alg\`ebre et de g\'eom\'etrie (online), 09 Feb. 2021, Invited

  
• Positivity of an analog of Kazhdan-Lusztig polynomials for finite-dimensional representations of quantum affine algebra

  Ryo Fujita

  Lie theory seminar (online), 02 Feb. 2021, Invited

  
• Twisted Auslander-Reiten quivers, quantum Cartan matrix and representation theory of quantum affine algebras

  Ryo Fujita

  S\'eminaire d'alg\`ebre (online), 12 Oct. 2020, Invited

  
• Singularities of R-matrices, graded quiver varieties and generalized quantum affine Schur-Weyl duality

  Ryo Fujita

  Minami-Osaka Daisuu Seminar (online), 22 May 2020, Invited

  
• Singularities of R-matrices, graded quiver varieties and generalized quantum affine Schur-Weyl duality

  Ryo Fujita

  Representation Theory Seminar (online), 28 Apr. 2020, Invited

  
• Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

  Ryo Fujita

  Workshop on Quiver varieties, character varieties and DT-invariants, 27 Feb. 2020, Invited

  
• Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

  Ryo Fujita

  Workshop on Geometric Representation Theory and Quantum Field Theories, 20 Dec. 2019, Invited

  
• On the singularity of R-matrices between fundamental modules of type ADE

  Ryo Fujita

  Handayama Seminar on Geometry and Algebra, 05 Dec. 2019, Invited

  
• Graded quiver varieties and normalized R-matrices for fundamental modules

  Ryo Fujita

  RIMS Workshop: Representation Theory of Algebraic Groups and Quantum Groups, 23 Oct. 2019, Invited

  
• Quantum affine Schur-Weyl duality associated with a Dynkin quiver

  Ryo Fujita

  Autumn meeting of MSJ, 2019, 17 Sep. 2019, Invited

  
• Coherent IC-sheaves on type $A_{n}$ affine Grassmannians and the dual canonical basis of affine type $A_{1}$ (Poster presentation)

  Ryo Fujita

  Cluster Algebra 2019, 21 Jun. 2019

  
• Equivariant $K$-ring of $GL_n$ affine Grassmannian and a quantum unipotent cell of $LSL_2$

  Ryo Fujita

  Algebraic Lie Theory and Representation Theory 2019, 26 May 2019

  
• Coherent IC-sheaves on type $A_n$ affine Grassmannians and dual canonical basis of affine type $A_1$

  Ryo Fujita

  MS seminar, 11 Apr. 2019, Invited

  
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  Infinite Analysis 19: Quantum symmetries and integrable systems, 05 Mar. 2019, Invited

  
• Coherent IC-sheaves on type $A_n$ affine Grassmannians and dual canonical basis of affine type $A_1$

  Ryo Fujita

  Mini-workshop on representation theory, 14 Feb. 2019, Invited

  
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  Conference on Algebraic Representation Theory, 30 Nov. 2018, Invited

  
• Geometric realization of Dynkin quiver type Schur-Weyl duality

  Ryo Fujita

  Infinite dimensional algebras, geometry and integrable systems, 04 Nov. 2018, Invited

  
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  The 4th KTGU Mathematics Workshop for Young Researchers, 29 Sep. 2018

  
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  AMS-CMS Joint International Meeting, Special Session ``Geometric Representation Theory and Langlands Program'', 19 Jun. 2018, Invited

  
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  Seminar on Mathematical Physics, 18 Apr. 2018, Invited

  
• Affine highest weight categories and Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  Annual meeting of MSJ, 2018, 19 Mar. 2018

  
• Tilting modules in affine highest weight categories and the Arakawa-Suzuki functor

  Ryo Fujita

  Annual meeting of MSJ, 2018, 19 Mar. 2018

  
• Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Dujita

  23th Daisuu Wakate Meeting, 08 Mar. 2018

  
• On the structure of a certain module category of quantum loop algebras of type ADE

  Ryo Fujita

  The 14th Mathematics Conference for Young Researchers, 27 Feb. 2018

  
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality (Poster presentation)

  Ryo Fujita

  The 3rd KTGU Mathematics Workshop for Young Researchers, 17 Feb. 2018

  
• Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  The 1st Mathsci Freshman Seminar, 14 Jan. 2018

  
• Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types

  Ryo Fujita

  S\'eminaire d'alg\`ebre, 08 Jan. 2018, Invited

  
• Affine highest weight categories for quantum loop algebras of Dynkin types

  Ryo Fujita

  Minami-Osaka Daisuu Seminar, 29 Nov. 2017, Invited

  
• Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types

  Ryo Fujita

  Representation Theory Seminar, 15 Nov. 2017, Invited

  
• Affine highest weight structure and Dynkin quiver type quantum affine Schur-Weyl duality

  Ryo Fujita

  Shinshu Algebra Seminar, 06 Nov. 2017, Invited

  
• Affine highest weight categories for quantum loop algebras of Dynkin types

  Ryo Fujita

  Kyoto Representation Theory Seminar, 05 Oct. 2017, Invited

  
• Affine highest weight category and Schur-Weyl duality

  Ryo Fujita

  Algebra Seminar, 05 Sep. 2017, Invited

  
• Tilting modules in affine highest weight categories

  Ryo Fujita

  Algebraic Lie Theory and Representation Theory 2017, 11 Jun. 2017

  
• Tilting modules in affine highest weight categories

  Ryo Fujita

  Lie Theory Seminar, 07 Mar. 2017, Invited

  
• Tilting modules in affine highest weight category and applications (Poster presentation)

  Ryo Fujita

  The 14th Kinosaki Freshman Seminar, 15 Feb. 2017

  
• Tilting modules in affine highest weight category and applications

  Ryo Fujita

  Kobe Seminar on Integrable Systems, 14 Dec. 2016, Invited

  
• Arakawa-Suzuki functor on the deformed BGG category of $\mathfrak{gl}_m$

  Ryo Fujita

  Conference on Algebraic Representation Theory, 05 Dec. 2016, Invited

  
• The Arakawa-Suzuki functor on the deformed BGG category of the general linear Lie algebra

  Ryo Fujita

  Symposium on Representation Theory, 02 Dec. 2016

  
• Tilting modules of affine quasi-hereditary algebras

  Ryo Fujita

  Kyoto Representation Theory Seminar, 07 Oct. 2016, Invited

  
• Deformed BGG category and Schur-Weyl duality (Poster presentation)

  Ryo Fujita

  The 13th Kinosaki Freshman Seminar, 27 Feb. 2016

  

External funds: Kakenhi

• Noncommutative monoidal categories arising from affine quantum groups and their variants

  Grant-in-Aid for Early-Career Scientists

  Basic Section 11010:Algebra-related

  Kyoto University

  藤田 遼

  From 01 Apr. 2026, To 31 Mar. 2030, Granted

  モノイダル圏;アフィン量子群;テンソル積表現;R行列;団代数

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-26K16962/
• Study on the representations of affine quantum groups using quivers with potentials

  Grant-in-Aid for Early-Career Scientists

  Basic Section 11010:Algebra-related

  Kyoto University

  藤田 遼

  From 01 Apr. 2023, To 31 Mar. 2026, Granted

  アフィン量子群;R行列;ディンキン箙;E不変量;団代数;量子グロタンディーク環;標準基底;箙ヘッケ環;量子Grothendieck環;モノイダル型Jantzenフィルトレーション;ポテンシャル付箙;団代数の圏化;箙多様体;Kirillov-Reshetikhin加群

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K12955/
• Representation theory of vertex algebras for the 21st century

  Grant-in-Aid for Scientific Research (S)

  Broad Section B

  Kyoto University

  荒川 知幸

  From 05 Jul. 2021, To 31 Mar. 2026, Granted

  頂点作用素代数;表現論;4D/2D双対性;W代数;4次元の超対称性場の理論;4次元の場の理論;随伴多様体;4 次元の超対称性場の理論;群の表現論

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21H04993/

Education

Teaching subject(s)

• From 01 Apr. 2025, To 31 Mar. 2026

  Mathematical Theory of Symmetries

  N177, Fall, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2024, To 31 Mar. 2025

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2