T. Nakanishi

activity

20242026

collaborators

4 papers

math.RT2026

Relation between generalized and ordinary cluster algebras

Ryota Akagi, Tomoki Nakanishi

Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their i…

math.RA2025

Cluster Algebras and Dilogarithm Identities

Tomoki Nakanishi

This is a reasonably self-contained exposition of the fascinating interplay between cluster algebras and the dilogarithm in the past two decades. The dilogarithm has a long and ric…

hep-th2024

$S^{1}$ reduction of 4D $N = 4$ Schur index and 3D $N = 8$ mass-deformed partition function

Tomoki Nakanishi, Takahiro Nishinaka

We study the compactification of 4D $N = 4$ SYM on $S^{1}$ from the viewpoint of the superconformal index. In the cases that the gauge group of the 4D SYM is $U (N)$ and $Usp(…

math.CO2024

Local and global patterns of rank 3 $G$ -fans of totally-infinite type

Tomoki Nakanishi

We focus on the $G$ -fans associated with cluster patterns whose initial exchange matrices are of infinite type. We study the asymptotic behavior of the $g$ -vectors around the initi…

Relation between generalized and ordinary cluster algebras

Cluster Algebras and Dilogarithm Identities

S1 reduction of 4D N=4 Schur index and 3D N=8 mass-deformed partition function

Local and global patterns of rank 3 G-fans of totally-infinite type

$S^{1}$ reduction of 4D $N = 4$ Schur index and 3D $N = 8$ mass-deformed partition function

Local and global patterns of rank 3 $G$ -fans of totally-infinite type