Fujita, Ryo(Research Institute for Mathematical Sciences (RIMS)) | Activity Database on Education and Research, Kyoto University

Fujita, Ryo

Research Institute for Mathematical Sciences (RIMS) Assistant Professor

Last Updated :2025/05/02

Basic Information

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 the representation theory of algebras related to complex semisimple Lie algebras and their root systems, mainly, affine quantum groups.

RIMS profile page. arXiv. Google Scholar.

ID,URL

ORCID ID
0000-0003-4905-2402
J-Global ID
202001010407465468
Researcher number
40972477

researchmap URL

https://researchmap.jp/ryo_fujita

Last Updated :2025/05/02

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

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.

Inflations among quantum Grothendieck rings of type A
Ryo Fujita
Preprint arXiv:2412.11881, 16 Dec. 2024

Singularities of normalized R-matrices and E-invariants for Dynkin quivers
Ryo Fujita
Preprint arXiv:2410.10070, 14 Oct. 2024

Monoidal Jantzen filtrations
Ryo Fujita; David Hernandez
Preprint arXiv:2402.13544, 22 Feb. 2024

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

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

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;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 次元の超対称性場の理論;群の表現論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21H04993/

Last Updated :2025/05/02

Education

Teaching subject(s)

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

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