Dyson's Brownian motion model with $\beta=2$ was originally introduced as an eigenvalue process of Hermitian-matrix-valued Brownian motion in random matrix theory. Grabiner (1999) constructed it as the Doob $h$-transform of absorbing Brownian motion in a Weyl chamber and realized it as a system of one-dimensional Brownian motions conditioned never to collide with each other (the noncolliding Brownian motion). By replacing the rational functions appearing in the $h$-transform with the elliptic functions having time-dependent nomes $q=q(t)$, we introduced an elliptic extension of the Dyson model, which is an inhomogeneous diffusion process of noncolliding particles defined on a circle in a finite time period $[0, t_*)$, $0 < t_* < \infty$. When the process starts from the configuration with equidistant spacing on the circle (denoted by $\eta$), we gave a determinantal martingale representation and proved that the process is determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single continuous function called the correlation kernel (to appear in PTRF, DOI 10.1007/s00440-014-0581-9). In the present talk, we put emphasis on the important role of Jacobi's imaginary transformations (the modular transformations) in such `elliptic-functional diffusion processes' and show that our process can be regarded as a system of noncolliding Brownian bridges of length $t_*$ from $\eta$ to $\eta$. An infinite particle limit will be also discussed.
