Publication

Published papers

1. On a Nielsen-Thurston classification theory for cluster modular groups, Annales de l'Institut Fourier 69 (2019) no. 2 p. 515-560. [article link]

2. Presentations of cluster modular groups and generation by cluster Dehn twists, SIGMA 16 (2020), 025, 22 pages. [article link]

3. Algebraic entropy of sign-stable mutation loops, with Shunsuke Kano, Geom. Dedicata 214, 79–118 (2021). [article link]

4. Cluster realizations of Weyl groups and higher Teichmüller theory, with Rei Inoue and Hironori Oya, Sel. Math. New Ser. 27, 37 (2021). [article link]

5. Skein and cluster algebras of unpunctured surfaces for  𝔰𝔩(3), with Wataru Yuasa,  Math. Z. 303, 72 (2023). [article link]

6. 𝒜=𝒰 for cluster algebras from moduli spaces of G-local systems, with Hironori Oya and Linhui Shen, Adv. Math. 431, 109256 (2023). [article link]

7. Wilson lines and their Laurent positivity, with Hironori Oya, Math. Z. 305, 34 (2023). [article link]

8. Earthquake theorem for cluster algebras of finite type, with Takeru Asaka and Shunsuke Kano,  Int. Math. Res. Not., rnae027 (2024). [article link]

Preprints

1. Sign stability of mapping classes on marked surfaces I: empty boundary case, with Shunsuke Kano, preprint. [arXiv:2010.05214]

2. Sign stability of mapping classes on marked surfaces II: general case via reductions, with Shunsuke Kano, preprint. [arXiv:2011.14320]

3. Unbounded 𝔰𝔩(3)-laminations and their shear coordinates, with Shunsuke Kano, preprint. [arXiv:2204.08947]

4. Skein and cluster algebras of unpunctured surfaces for 𝔰𝔭(4), with Wataru Yuasa, preprint. [arXiv:2207.01540]

5. Teichmüller and lamination spaces with pinnings, preprint. [arXiv:2212.14780]

6. Quantum duality maps, skein algebras and their ensemble compatibility, with Hiroaki Karuo, preprint. [arXiv:2305.19074]

7. Skein and cluster algebras with coefficients for unpunctured surfaces, with Shunsuke Kano and Wataru Yuasa, preprint. [arXiv:2312.02861]

8. Entropy of cluster DT transformations and the finite-tame-wild trichotomy of acyclic quivers, with Shunsuke Kano, preprint. [arXiv:2403.01396]

9. Unbounded 𝔰𝔩(3)-laminations around punctures, with Shunsuke Kano, preprint. [arXiv:2404.18236]

Thesis

Geometry of cluster modular groups, Ph.D. thesis in the University of Tokyo (2020).

Proceedings

1. Cluster Dehn twists in cluster modular groups, Intelligence of Low-Dimensional Topology, RIMS Kôkyûroku No.2099

2. Wilson Lines and Their Laurent Positivity, Lie theory and its applications in physics, Varna, Bulgaria, June 2021. Papers from the 14th Workshop (LT-14) held June 20–26. Edited by Vladimir Dobrev. Springer Proceedings in Mathematics & Statistics, 335. Springer, Singapore, [2021], ©2022. 

3. Stratifications of the moduli space of decorated G-local systems and their relation to braid varieties, ALTReT 2023. [File]

Interdisciplinary works

1. Geometric description of lattice defects via singular affine manifolds, 数理科学実践研究レター2019 (Japanese). [article link]