Publications

Keywords

Targets  
     
mathematical physics  >  integrable system 
          
>  Toda lattice,  Mumford system,  Box-ball system,
T/Y-system 
      knot invariants  >  complex volume

Methods
      algebraic geometry, tropical geometry  >  Jacobi variety,  Riemann's theta function
      quantum group > crystal base
      cluster algebra


Preprints

Toric networks, geometric R-matrices and generalized discrete Toda lattices
(with Thomas Lam and Pavlo Pylyavskyy)
arXiv:1504.03448

Papers (2000~)

Braids, Complex Volume, and Cluster Algebra
(with Kazuhiro Hikami) Algebraic and Geometric Topology, to appear.
arXiv:1304.4776

Braiding Operator via Quantum Cluster Algebra
(with Kazuhiro Hikami) J. Phys. A: Math. Theor., 47, 474006 (2014).
arXiv:1404.2009

Discrete Painlevé equations from Y-systems
(with Andrew N. W. Hone) J. Phys. A: Math. Theor., 47, 474007 (2014).
arXiv:1405.5379

Algebraic integrable systems related to spectral curves with automorphisms
(with Pol Vanhaecke and Takao Yamazaki) J. Geom. Phys., 87, 198-216 (2015).
arXiv:1312.4208

Cluster Algebra and Complex Volume of Once-Punctured Torus Bundles and Two-Bridge Knots
(with Kazuhiro Hikami) J. Knot Theory and Its Ramifications,  23, 1450006 [33 pages] (2014).
arXiv.1212.6042.


Tropical curves and integrable piecewise linear maps
(with Shinsuke Iwao) Contemp. Math., 580,
pp. 21-39 (2012).
arXiv:1111.5771.

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
(with Atsuo Kuniba and Taichiro Takagi) (a review article)
J. Phys. A, 45, 073001 (2012).

arXiv:1109.5349.

Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
(with Tomoki Nakanishi)
RIMS Kokyuroku Bessatsu, B28, pp 63 - 88 (2011).
arXiv:1012.5574.

Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2
(with Osamu Iyama, Bernhard Keller, Atsuo Kuniba and Tomoki Nakanishi)
Publ. RIMS 49, pp 43 - 85 (2013).
arXiv:1001.1881.

Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r

(with Osamu Iyama, Bernhard Keller, Atsuo Kuniba and Tomoki Nakanishi)
Publ. RIMS 49, pp 1 - 42 (2013).
arXiv:1001.1880.

Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice
(with Shinsuke Iwao) in "Proceedings of the Infinite Analysis 09: New Trends in Quantum Integrable
Systems", eds. B. Feigin, et al., pp. 101 - 116 (World Scientific, 2011).

arXiv:1003.0057.

Singular fiber of the Mumford system and rational solutions to the KdV hierarchy
(with
Pol Vanhaecke and Takao Yamazaki) Comm. Pure Appl. Math., 63, Issue 4, pp 508 - 532 (2010).
arXiv:0806.2362.

Periodicities of T-systems and Y-systems
(with Osamu Iyama, Atsuo Kuniba, Tomoyuki Nakanishi and Junji Suzuki)
Nagoya Mathematical Journal, 197, pp 59 - 174 (2010).
arXiv:0812.0667.

Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic
(with Tomoyuki Takenawa) RIMS Kokyuroku Bessatsu, B13, pp 175 - 190 (2009).
arXiv:0902.0448.

A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice
(with Tomoyuki Takenawa) Comm. Math. Phys., 289, pp 995 - 1021 (2009).
arXiv.0806.3318.

Tropical spectral curves and integrable cellular automata
(with Tomoyuki Takenawa) Int. Math. Res. Not. IMRN, vol. 2008, rnn019, 27 pages (2008).
arXiv.0704.2471.

Multi-Hamiltonian structures on Beauville's integrable system and its variant
(with Yukiko Konishi) SIGMA Symmetry Integrability Geom. Methods Appl., 3, 007, 16 pages (2007).

Jacobian variety and integrable system --- after Mumford, Beauville and Vanhaecke
(with
Yukiko Konishi and Takao Yamazaki) J. Geom. Phys., 57, pp 815 - 831 (2007).
math-ph/0512033.

Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system
(with
Takao Yamazaki) Comm. Math. Phys., 265, pp 699 - 719 (2006).
math-ph/0501048.

A quantization of box-ball systems
(with
Atsuo Kuniba and Masato Okado) Rev. Math. Phys., 16, pp 1227 - 1258 (2004).

The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice
J. Phys. A: Math. Gen., 37, pp 1277 - 1298 (2004).

The extended Lotka-Volterra lattice and affine Jacobi varieties of spectral curves
J. Math. Phys., 44, pp 338 - 351 (2003).

The lattice Toda field theory for simple Lie algebras
Contemp. Math., 309, pp 115 - 128 (2002).

The lattice Toda filed theory and lattice W algebras for B2 and C2
J. Phys. A: Math. Gen., 35, pp 1013 - 1024 (2002).

Symmetry of integrable cellular automaton
(with
Kazuhiro Hikami) J. Phys. A: Math. Gen., 34, pp 2467 - 2476 (2001).

The A_M^{(1)} automata related to crystals of symmetric tensors
(with
Goro Hatayama, Kazuhiro Hikami, Atsuo Kuniba, Taichiro Takagi and Tetsuji Tokihiro)
J. Math. Phys., 42, pp 274 - 308 (2001).

The lattice Toda field theory for simple Lie algebras --- Hamiltonian structure and tau-function
(with
Kazuhiro Hikami) Nucl. Phys. B, 581 [PM], pp 761 - 775 (2000).

Supersymmetric extention of the integrable box-ball system
(with
Kazuhiro Hikami) J. Phys. A: Math. Gen., 33, pp 4081 - 4094 (2000).